Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms

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Kerala State Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms

Decimal Forms Text Book Questions and Answers

Measuring length Textbook Page No. 73

Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 1
What is length of this pencil?
6 centimetres and 7 millilitres.
How about putting it in millimetres only? 67 millimetres.
Can you say it in centimetres only?
One centimetre means 10 millimetres.
Putting it the other way round, one millimetre is a tenth of a centimetre.
That is, \(\frac{1}{10}\) centimetre
1 millilitre = \(\frac{1}{10}\) centimetre
So, 7 millimetres is \(\frac{7}{10}\) centimetres.
Now can’t you say the length of the pencil in just centimetres?
6 centimetres, 7 millilitres = 6\(\frac{7}{10}\) centimetres.

We also write this as 6.7 centimetre. To be read 6 point 7 centimetre. It is called the decimal form of 6\(\frac{7}{10}\) centimetres.

Like this, 7 centimetre, 9 millimetre is \(\frac{9}{10}\) centimetre. And we write it as 7.9 centimetre in decimal form.

Now measure the length of your pencil and write it in decimal form.

My pencil is exactly 8 centimetres. How do I write it in decimal form?
Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 2

Just write 8.0
Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 3

Since in 8 centimetres, there is no millimetre left over, we may write it as 8.0 centimetres also.
Lengths less than one centimetre is put as only millimetres. How do we write such lengths as centimetres?
Answer:
8.0 centimetres,

Explanation:
We write 8 centimetres in decimal form as 8.0 centimetres.

For example, 6 millimetres means \(\frac{6}{10}\) centimetres and so we write it as 0.6 centimetres (read 0 point 6 centimetres)
Like this, 4 millimetre = \(\frac{4}{10}\) centimetre = 0.4 centimetre.

Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms

Different measures

Lengths greater than one centimetre are usually said in metres. How many centimetres make a metre?
In reverse, what fraction of a metre is a centimetre?
1 centimetre = \(\frac{1}{100}\) metre.
Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 4

Sajin measured the length of a table as 1 metre and 13 centimetres. How do we say it in metres only?

13 centimetres means \(\frac{13}{100}\) of a metre.
That is, \(\frac{13}{100}\) metre.
1 metre and 13 centimetre means 1\(\frac{13}{100}\) metre. We can write this us 1.13 metres in decimal form.
Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 5
Like this,
3 metres, 45 centimetres = 3\(\frac{45}{100}\) metre = 3.45 metres.
Now how do we write 34 centimetres in terms ola metre?
34 centimetre = \(\frac{34}{100}\) metre = 0.34 metre.

Vinu measured the length of a table as 1 metre, 12 centimetres, 4 millimetres.
How do we say it in terms of a metre?
12 centimetres means 120 millimetres.
With 4 millimetres more, it is 124 millimetres.
1 millimetre is \(\frac{1}{100}\) of a metre.
So, 124 millimetres = \(\frac{124}{100}\) metre.
1 metre and 124 millimetre together is 1\(\frac{124}{100}\) metre.
Its decimal form is 1.124 metre.
Thus 5 metre, 32 centimetres, 4 millimetres in decimal form is,
5 metre, 324 millilitre = 5\(\frac{324}{1000}\) = 5.324 metre.

Millimetre and metre
1 m = 100 cm
1 cm = 10 mm
1 m = 1000 mm
So,
1 cm = \(\frac{1}{100}\) m
1 mm = \(\frac{1}{10}\) cm
1 mm = \(\frac{1}{1000}\) m

We can write other measurements also in the decimal form.
One gram is \(\frac{1}{1000}\) of a kilogram.
So, 5 kilograms and 315 grams we can write as 5\(\frac{315}{1000}\) kilograms.
Its, decimal form is 5.3 15 kilograms.

Like this,
4 grams 250 milligrams = 4\(\frac{250}{100}\) gram = 4.250 grams.
A millilitre is \(\frac{1}{1000}\) litre.
So,
725 millilitre = \(\frac{725}{1000}\) litre = 0.725 litre.

Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms

Write the following measurements in fractional and in decimal form.
Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 6
Answer:
Kerala State Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms-1

Explanation:
Wrote the given measurements in fractional and in decimal form above as 1. 4 cm 3 mm in fractional form is as 1 cm = 10 mm so 4 X 10 mm + 3 mm = 40 + 3 = 43 mm or \(\frac{43}{1}\) mm and in decimal form is 4.3 cm, 2. 5 mm in fractional form is as 1 mm = \(\frac{1}{10}\) cm so it is \(\frac{5}{10}\) cm and in decimal form it is 0.5 cm, 3. 10 m 25 cm in fractional form is as 1 cm = \(\frac{1}{100}\) m so it is \(\frac{1025}{100}\) m and in decimal form it is 10.25 m, 4. 2 kg 125 g in fractional form as 1 g = \(\frac{1}{1000}\) kg is \(\frac{2125}{1000}\) kg and in decimal form it is 2.125 kg, 5. 16 l 275 ml in fractional form as 1 ml = \(\frac{1}{1000}\) l so it is \(\frac{16275}{1000}\) l in decimal form it is 16.275 l, 6. 13l 225 ml in fractional form as 1 ml = \(\frac{1}{1000}\) l so it is \(\frac{13225}{1000}\) l in decimal form it is 13.225 l 7. 325 ml in fractional form is as 1 ml = \(\frac{1}{1000}\) l so it is \(\frac{325}{1000}\) l in decimal form it is 0.325 l.

In reverse Textbook Page No. 77

Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 7

1.45 metre as a fraction is 1\(\frac{45}{1000}\) metre.
How much in metre and centimetre?
1 metre 45 centimetre.
That is 145 centimetres.
So, 1.45 metre means 145 centimetres.
Like this, how about writing 0.95 metre in centimetre?
How much centimetre is this?
Answer:
145 centimetre shirt, 95 centimetre pants,

Explanation:
Given 1.45 metre for a shirt, 0.95 metre for pants, So in centimetres 1 m is equal to 100 centimetre so 1.45 metre is 100 + 45 = 145 centimetre for shirt. Now 0.95 metre = 0.95 X 100 centimetre = 95 centimetre pants.

Next try converting 0.425 kilograms into grams?
Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 8
0.425 kilograms = \(\frac{425}{1000}\) kilograms = 425 gram.

Fill up the table.

Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 9
Answer:
Kerala State Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms-2

Explanation:
Filled the given table as shown above,1) 3.2 cm in expanded form is as 1 cm = 10 mm so 3 X 10 mm + 2 mm = 32 mm and 1 mm = \(\frac{1}{10}\) cm, the fraction form is 3\(\frac{2}{10}\) cm, 2) 1 mm = \(\frac{1}{10}\) cm so 7 mm = \(\frac{7}{10}\) cm and in decimal form it is 0.7 cm, 3) 3.41 m in expanded form is as 1 m = 100 cm so 3 X 100 cm + 41 cm = 341 cm and 1 cm = \(\frac{1}{100}\) m, the fraction form is 3\(\frac{41}{100}\) cm, 4) \(\frac{62}{10}\) m = 6.2 m and 1m = 100 cm so 6.2 m = 6.2 X 100 = 620 cm, 5) 5.346 kg in expanded form is as 1 kg = 1000 g so 5 X 1000 g + 346 g = 5346 g and 1 kg =1000 g, the fraction form is \(\frac{5346}{1000}\) kg, 6) 1 kg = 1000 g and 1 g = \(\frac{1}{1000}\) kg so 425 g in decimal form is 0.425 kg and in fractional form is \(\frac{425}{1000}\) kg, 7) 2.375 l in expanded form is as 1 l = 1000 ml so 2 x 1000 ml + 375 ml = 2375 ml and 1 ml = \(\frac{1}{1000}\) l, the fraction form is \(\frac{2375}{1000}\) l, 8) 1.350 l in expanded form is as 1 l = 1000 ml so 1 X 1000 ml + 350 ml = 1350 ml and 1 ml = \(\frac{1}{1000}\) l, the fraction form is \(\frac{1350}{1000}\) l, 9) 1 l = 1000 ml and 1 ml = \(\frac{1}{1000}\) l then \(\frac{625}{1000}\) l in decimal form is 0.625 l and in expanded form 0.625 l X 1000 ml = 625 ml.

Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms

One fractions, many from

The heights of the children in a class are recorded. Ravi is 1 metre, 34 centimetre tall. This was written 1.34 metres. Naufal is 1 metre, 30 centimetres tall and this was written 1.30 metres.
Lissi had a doubt!
30 centimetres means \(\frac{30}{1000}\) metre. This can be written \(\frac{3}{10}\) metre.
So, why not write Ravi’s height as 1.3 metres?

“Both are right,” the teacher said.
Since, \(\frac{3}{10}\) = \(\frac{30}{100}\), we can write the decimal form of \(\frac{3}{10}\) as 0.3 or 0.30.
Then Ravi had a doubt: Since \(\frac{3}{10}\) = \(\frac{300}{1000}\), we can write, 30 centimetres as 0.300 metres.
“It is also right,” the teacher continued. How we write decimals is a matter of convenience.

For example, look at some lengths measured in metre and centimetre.
1 metre 25 centimetres
1 metre 30 centimetres
1 metre 32 centimetres
It is convenient to write these like this:
1.25 metre
1.30 metre
1.32 metre

If we measure millimetres also like this:
1 metre 25 centimetres 4 millimetres
1 metre 30 centimetres
1 metre 32 centimetres
It is better to write them as:
1.254 metre
1.300 metre
1.320 metre
Like this how can we write the decimal form of 2 kilogram, 400 gram?
What about 3 litres. 500 millilitres?
Answer:
2.400 kilograms, 3.500 litres,

Explanation:
1 kilogram = 1000 grams so 400 grams = \(\frac{400}{1000}\) kilogram then 2 kilogram + 0.400 kilograms = 2.400 kilograms, 1 litre = 1000 millilitres so 500 millilitres = \(\frac{500}{1000}\) litre then 2 litres + 0.400 litres = 2.400 litres and 3 litres.500 millilitres = 3.500 litres.

Place value Textbook Page No. 80

We have seen how we can write various measurements as fractions and in decimal forms.
If we look at just the numbers denoting these measurements, we see that they are fractions with 10, 100, 1000 so on as denominators.

For example, just as we wrote 2 centimetres, 3 millimetres as 2\(\frac{3}{10}\) and then as 2.3, we can write 2\(\frac{3}{10}\) as 2.3, whatever, be the measurement.
That is, 2.3 is the decimal form of 2\(\frac{3}{10}\).
Similarly, 4.37 is the decimal from of 4\(\frac{37}{100}\)
We can write
2\(\frac{3}{10}\) = 2.3
4\(\frac{37}{100}\) = 4.37
and so on.

On the otherhand, numbers in decimal form can be written as fractions:
247.3 = 247\(\frac{3}{10}\) = 247 + \(\frac{3}{10}\)
The number 247 in this can be split into hundreds, tens and ones:
247 = (2 × 100) + (4 × 10) + (7 × 1)
So, we can write 247.3 as
247.3 = (2 × 100) + (4 × 10) + (7 × 1) + (3 × \(\frac{1}{10}\))
How about 247.39?

First we write
247.39 = 247\(\frac{39}{100}\) = 247 + \(\frac{39}{100}\)
Then split \(\frac{39}{100}\) like this:
\(\frac{39}{100}\) = \(\frac{30+9}{100}\) = \(\frac{30}{100}\) + \(\frac{9}{100}\) = \(\frac{3}{10}\) + \(\frac{9}{100}\) = (3 × \(\frac{1}{100}\)) + (9 × \(\frac{1}{100}\))
So, we can write 247.39 like this
247.39 = (2 × 100) + (4 × 10) + (7 × 1) + (3 × \(\frac{1}{10}\)) + (9 × \(\frac{1}{100}\))
In general, we can say this:

In a decimal form, we put the dot to separate the whole number part and the fraction part. Digits to the left of the dot denote multiples of one. ten, hunded and so on; digits on the right denote multiples of tenth, hundredth, thousandth and so on.

For example. 247.39 can be split like this:
Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 10
Can you split the numbers below like this.
1.42 16.8 126.360 1.064 3.002 0.007
Answer:
Yes we can split the numbers,

Explanation:
Kerala-Syllabus-6th-Standard-Maths-Solutions-Chapter-5-Decimal-Forms-10
1.42 = (1 X 1) + (4 X \(\frac{1}{10}\)) + (2 X \(\frac{1}{100}\)),
Kerala-Syllabus-6th-Standard-Maths-Solutions-Chapter-5-Decimal-Forms-12
16.8 = (1 X 10) + (6 X 1) + (8 X \(\frac{1}{10}\)),
Kerala-Syllabus-6th-Standard-Maths-Solutions-Chapter-5-Decimal-Forms-13
126.360 = (1 X 100) + (2 X 10) + (6 X 1) + (3 X \(\frac{1}{10}\)) + (6 X \(\frac{1}{100}\)),Kerala-Syllabus-6th-Standard-Maths-Solutions-Chapter-5-Decimal-Forms-15
1.064 = (1 X 1) + (0 X \(\frac{1}{10}\)) + (6 X \(\frac{1}{100}\)) + (4 X  \(\frac{1}{1000}\)),
Kerala-Syllabus-6th-Standard-Maths-Solutions-Chapter-5-Decimal-Forms-16
3.002 = (3 X 1) + (0 X \(\frac{1}{10}\)) + (0 X \(\frac{1}{100}\)) + (2 X \(\frac{1}{1000}\)),
Kerala-Syllabus-6th-Standard-Maths-Solutions-Chapter-5-Decimal-Forms-17
0.007 = (0 X 1) + (0 X \(\frac{1}{10}\)) + (0 X \(\frac{1}{100}\)) + (7 X \(\frac{1}{1000}\)).

Fraction and decimal Textbook Page No. 81

\(\frac{1}{2}\) centimetres means, 5 millimetres. Its decimal form is 0.5 centimetre. So the decimal form of the fmction \(\frac{1}{2}\) is 0.5
\(\frac{1}{2}\) = \(\frac{5}{10}\) right?
Similarly, what is the decimal form of \(\frac{1}{5}\)?

Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms

Measurements again

Let’s look at the decimal form of some measurements again. For example, what is the decimal form of 23 metre, 40 centimetre. As seen earlier.
23 metre 40 centimetre = 23\(\frac{40}{100}\) metre = 23.40 metre

Looking at just the numbers;
\(\frac{40}{100}\) = \(\frac{4}{100}\)
23\(\frac{40}{100}\) = 23\(\frac{4}{10}\) = (2 X 10) + (3 X 1) + (4 X \(\frac{4}{10}\)) = 23.4
So, we can write 23 metre, 40 centimetre either as 23.40 metre or as 23.4 metre.
What about 23 metre, 4 centimetre?
23 metre 4 centimetres = 23\(\frac{4}{100}\) metre
Writing just the numbers,
23\(\frac{4}{100}\) = (2 X 10) + (3 X 1) + (4 X \(\frac{1}{100}\))
= (2 X 10) + (3 X 1) + (0 X \(\frac{1}{10}\)) + (4 X \(\frac{1}{100}\))
= 23.04
Here the 0 just after the dot shows that the fractional part of the number has no tenths (The 0 in 307 shows that, after 3 hundreds, this number has no tens, right?)

Thus we write 23 metres, 4 centimetres as 23.04 metres. How about 23 metres and 4 millimetres? 23 metres 4 millimetres
= 23\(\frac{4}{1000}\) metres
Writing only the numbers,
23\(\frac{4}{1000}\) = (2 X 10) + (3 X 1) + (4 X \(\frac{1}{1000}\))
= (2 X 10) + (3 X 1) + (0 X \(\frac{1}{10}\)) + (0 X \(\frac{1}{100}\)) + (4 X \(\frac{1}{1000}\))
= 23.004
Thus
23 metre 4 millimetres = 23.004 metre

Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms

Some other fractions 

We cannot write \(\frac{1}{4}\) as a fraction with denominator 10. But we have \(\frac{1}{4}\) = \(\frac{25}{100}\). So the decimal form of \(\frac{1}{4}\) is 0.25. What is the decimal form of \(\frac{3}{4}\)? And \(\frac{3}{8}\)?
Answer:
Decimal form of \(\frac{3}{4}\) is 0.75 and decimal form of \(\frac{3}{8}\) is 0.375,

Explanation:
Writing, \(\frac{3}{4}\) = \(\frac{3}{4}\) X \(\frac{25}{25}\) = \(\frac{75}{100}\) = 0.75 is the decimal form, \(\frac{3}{8}\) = \(\frac{3}{8}\) X \(\frac{125}{125}\) = \(\frac{375}{1000}\) = 0.375 is the decimal form.

Fill up this table.

Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 11
Answer:
Kerala-Syllabus-6th-Standard-Maths-Solutions-Chapter-5-Decimal-Forms-19

Explanation:
1) 45 cm in fraction form is \(\frac{45}{100}\) m because 1 m = 100 cm and in decimal form it is 0.45 m, 2) 315 g in fractional form is \(\frac{315}{1000}\) kg because 1 kg = 1000 g and in decimal form it is 0.315 g, 3) 455 ml in fractional form is \(\frac{455}{1000}\) ml because 1 l = 1000 ml and in decimal form it is 0.455 l, 4) \(\frac{5}{100}\) m in decimal form is 0.05 m while in measurement it is 5 centimetres because 1 m = 100 cm, 5) \(\frac{42}{1000}\) kg in decimal form is 0.042 kg and in measurement it is 42 grams because 1 kg = 1000 g, 6) 0.035 l in fractional form is \(\frac{35}{1000}\) l and in measurement it is 35 ml because 1l = 1000 ml, 7) 3kg 5g in fractional form can be written as \(\frac{3005}{1000}\) kg because 1kg = 1000 g so 3kg 5g = [(3 x 1000) + 5] g = 3005 g and in decimal form it is 3.005 g, 8) 2l 7ml in fractional form can be written as \(\frac{2007}{1000}\) l because 1l = 1000 ml so 2l 7 ml = [(2 X 1000) + 7] ml = 2007 ml and in decimal form it is 2.007 ml, 9)3m 4cm in fractional form can be written as \(\frac{304}{100}\) m because 1m = 100 cm so 3m 4cm = [(3 X 100) + 4] = 304 cm and in decimal form it is 3.04 m, 10) 3m 4mm in fractional form can be written as \(\frac{3004}{1000}\) m because 1m = 100 cm and 1mm = 0.1 cm and in decimal form it is 3.004 m, 11) 4kg 50g in fractional form can be written as \(\frac{4050}{1000}\) kg because 1 kg = 1000 g so 4kg 50g = [(4 x 1000) + 50] g = 4050g and in decimal form it is 4.050 g, 12) 4kg 5g in fractional form can be written as \(\frac{4005}{1000}\) kg because 1 kg = 1000 g so 4kg 5g = [(4 X 1000) + 5] g = 4005g and in decimal form it is 4.005 g, 13) 4kg 5mg in fractional form can be written as \(\frac{4000005}{1000}\) kg because 1 kg = 1000 g , 1 mg = 0.001 g so 4kg 5mg = [(4 X 1000) + 0.005] g = 4000.005 g and in decimal form it is 4.000005 g,14) 2ml in fractional form is \(\frac{2}{1000}\) ml because 1 l = 1000 ml and in decimal form it is 0.002 l, 15) 0.02l in fractional form is \(\frac{20}{1000}\) l because 1 l = 1000 ml and in measurement form it is 20 ml, 16) \(\frac{200}{1000}\) l in decimal form is 0.2l and in measurement form it is 200 ml because 1l = 1000 ml.

More and less 

Sneha’s height is 1.36 metre and Meena’s height is 1.42 metre. Who is taller?
In the sports meet, Vinu jumped 3.05 metres and Anu, 3.5 metres. Who won?
Vinu jumped 3 metres, 5 centimetres and Anu jumped 3 metres, 50 centimetres, right? So who won?
Answer:
Meena is taller,
Anu Won,

Explanation:
Given Sneha’s height is 1.36 metre and Meena’s height is 1.42 metre. Now if we compare Sneha’s height and Meena’s height 1.42 metre is more or greater than 1.36 metre so Meena is taller,
Now given Vinu jumped 3 metres, 5 centimetres and Anu jumped 3 metres, 50 centimetres, Comparing Vinu and Anu jumped heights if we see 3 metres 50 centimetres is more or greater than 3 metres 5 centimetres so Anu jumped more height therefore Anu won.

Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 12

Largest number
Which is the largest number among 4836, 568,97? What about these? 0.4836, 0.568, 0.97
We can also look at it like this. Both numbers have 3 in one’s place. The number 3.05 has zero in the tenth’s place while 3.50 has 5 in the tenth’s place. So 3.50 is the larger number.
Similarly which is the largest among 2.400 kilogram, 2.040 kilogram, 2.004 kilogram?
What about 0.750 litre and 0.075 litre.
Answer:
2.400 kilogram is largest among the given numbers, 0.750 litre is largest among the given numbers,

Explanation:
The numbers have 4 in tenth’s place. The number 2.040 has zero in the tenth’s place while 2.004 has 4 in the thousandth place. So 2.400 is the larger number. The numbers have 7 in tenth’s place. The number 0.075 has zero in the tenth’s place . So 0.750 is the larger number.

Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms

Textbook Page No. 84

Question 1.
Find the larger in each of the pairs given below:
i) 1.7 centimetre, 0.8 centimetre
Answer:
1.7 centimetre is larger,

Explanation:
In 1.7, 1 is in the one’s place while in 0.8, 0 is in the one’s place. So 1.7 is larger.

ii) 2.35 kilogram, 2.47 kilogram
Answer:
2.47 kilogram is larger,

Explanation:
In 2.47, 4 is in the tenth’s place while in 2.35, 3 is the tenth’s place. So 2.47 is larger.

iii) 8.050 litre, 8.500 litre
Answer:
8.500 litre is larger,

Explanation:
In 8.500 , 5 is in tenth’s place while in 8.050, 0 is in tenth’s place. So 8.500 is larger.

iv) 1.005 kilogram, 1.050 kilogram
Answer:
1.050 kilogram is larger,

Explanation:
In 1.050, 5 is in the hundredth place while in 1.005, 0 is in the hundredth place. So 1.050 is larger.

v) 2.043 kilometre, 2.430 kilometre
Answer:
2.430 kilometre is larger,

Explanation:
In 2.430, 4 is in tenth’s place while in 2.043, 0 is in tenth’s place. So 2.430 is larger.

vi) 1.40 metre, 1.04 metre
Answer:
1.40 metre is larger,

Explanation:
In 1.40, 4 is in the tenth’s place while in 1.04, 0 is in the tenth’s place. So 1.40 is larger.

vii) 3.4 centimetre, 3.04 centimetre
Answer:
3.4 centimetre is larger,

Explanation:
In 3.4, 4 is in the tenth’s place while in 3.04 , 0 is in the tenth’s place. So 3.4 is larger.

viii) 3.505 litre, 3.055 litre
Answer:
3.505 litre is larger,

Explanation:
In 3.505, 5 is in the tenth’s place while in 3.055 , 0 is in the tenth’s place. So 3.505 is larger.

Question 2.
Arrange each set of numbers below from the smallest to the largest.
i) 11.4, 11.45, 11.04, 11.48, 11.048
Answer:
11.04, 11.048, 11.4, 11.45, 11.48,

Explanation:
The number 11.4 has 4 in tenth’s place, the number 11.45 has 4 in tenth’s place, the number 11.04 has 0 in tenth’s place, the number 11.48 has 4 in tenth’s place, the number 11.048 has 0 in tenth’s place, comparing 11.04 and 11.048 we understand 11.04 has 0 in thousandth place while 11.048 has 8 so 11.04 is the smallest, among 11.4, 11.45, 11.48, 11.4 is least because 11.4 has 0 in it’s hundredth place while 11.45 and 11.48 have 5 and 8 respectively we know 8 is greater than 5 hence 11.48 is greater than 11.45. Therefore the order of numbers is 11.04, 11.048, 11.4, 11.45, 11.48.

ii) 20.675, 20.47, 20.743, 20.074, 20.74
Answer:
20.074, 20.47, 20.675, 20.74, 20.743,

Explanation:
The number 20.074 has 0 in it’s tenth place while the other given numbers don’t have so it the smallest of all given numbers, 20.47 is the next smallest number because it has 4 in it’s tenth place while others have 6 and 7 in tenth place we know 7 is greater than 6 therefore 20.675 is the next least number, among both 20.74 and 20.743 we find 4 in hundredth place while 3 in thousandth place in one number and 0 in other so 20.743 is greater than 20.74. Therefore the order of numbers is 20.074, 20.47, 20.675, 20.74, 20.743.

iii) 0.0675, 0.064, 0.08, 0.09, 0.94
Answer:
0.064, 0.0675, 0.08, 0.09, 0.94,

Explanation:
All the given numbers contain 0 in their tenth place so we need to check the hundredth place 0.064 and 0.0675 are the numbers with least hundredth place value when we check the thousandth place 7 is greater than 4 so 0.064 is the least and 0.0675 is the next least, among 0.08, 0.09, 0.094; 0.08 is least as 8 is less than 9 and when we compare 0.09 and 0.094 we find 0.09 has 0 in it’s thousandth place while 0.094 has 4 so 0.09 is least compared to 0.094. Therefore the order of numbers is 0.064, 0.0675, 0.08, 0.09, 0.94.

Which of 11.4, 11.47, 11.465 the largest?
We can write 11.4 as 11.400 and 11.47 as 11.470.
Now can’t we find the largest?
Answer:
11.4, 11.465, 11.47,

Explanation:
All the given numbers have 4 in their tenth place so 11.4 is least because the hundredth place of the number is 0 when hundredth place is compared between  11.465 and 11.47 then 11.47 is greater than 11.465 as 7 is greater than 6. Therefore the order of numbers is 11.4, 11.465, 11.47.

Addition and subtraction

A 4.3 centimetre long line is drawn and then extended by 2.5 centimetres.
Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 23
What is the length of the line now?
We can put the length in millimetres and add
4.3 cm = 43 mm
2.5 cm = 25 mm
Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 13
Total length 43 +25 = 68mm
Turning this back into centimetres, we get 6.8 centimetres.
We can do this directly, without changing to millimetres.
Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 14
What if we want to add 4.3 centimetres and 2.8 centimetres?
If we change into millimetres and add, we get 71 millimetres.
And turing back into centiemtes, it becomes 7.1 centimetres.

Can we do this also directly, without changing to millimetres?
Let’s add in terms of place value.
Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 15
The answer is 6 ones and 11 tenths; that is, 7 ones and
1 tenth. This we can write 7.1
Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 16
How do we add 4.3 metres and 2.56 metres?
We can change both to centimetres and add
Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 17
4.3 m = 430 cm
2.56 m = 256 cm
The length is 430 + 256 = 686 centimetres.
Changing back to metres, it is 6.86 metres.
Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 18
We can add directly, without changing to centimetres 4.30
(when we do this, it is convenient to write 4.3 as 4.30)
What if we want to add 4.3 metres and 2.564 metre?
We can change both to millimetres and add
4300 mm + 2564 mm = 6864 mm
6864 mm = 6.864 mm = 6864
Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 19
Or directly add.
Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 20

Generally speaking, to add measurements given in decimal form, it is better to make the number of digits in the decimal parts same; for this, we need only add as many zeros as needed.
Now look at this; if from a 12.4 centimetre long stick, a 3.2 centimetre piece is cut off, what is the length of the remaining part?

3 centimetres subtracted from 12 centimetres is 9 centimetres.
2 millimetres subtracted from 4 millimetres is 2 millimetres.
We can write it like this;
Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 21
How do we subtract 3.9 centimetres from 15.6 centimetres?
We cannot subtract 9 millimetres from 6 millimetres. So we look at 15.6 centimetres as 14 centimetres and 16 millimetre. 9 millimetres subtracted from 16 millimetres gives 7 millimetres.
Let’s write according to place values and subtract.
Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 22

Another example: A sack contains 16.8 kilograms sugar. From this, 3.750 kilogram is put in a bag. How much sugar remains in the sack? Write 16.8 kilogram as 16.8000 kilograms and try it.
Answer:
Sugar remains in the sack is 13.050 kilograms,

Explanation:
Given a sack contains 16.8 kilograms sugar. From this, 3.750 kilogram is put in a bag. So sugar remains in the sack we wrote 16.8 kilogram as 16.8000 kilograms and subtracted 3.750 kilograms we get 13.050 kilograms.
Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms- 33

Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms

Textbook Page No. 87

Question 1.
Sunitha and Suneera divided a ribbon between them. Sunitha got 4.85 metre and Suneera got 3.75 metre. What was the length of the original ribbon?
Answer:
Total length of the ribbon is 8.60 metre,

Explanation:
Length of ribbon Sunitha has = 4.85 metre, Length of ribbon Suneera has = 3.75 metre, Total length of ribbon = 4.85 metre + 3.75 metre = 8.60 metre.
Kerala-Syllabus-6th-Standard-Maths-Solutions-Chapter-5-Decimal-Forms-18

Question 2.
The sides of a triangle are of lengths 12.4 centimetre, 16.8 centimetre, 13.7 centimetre. What is the perimeter of the triangle?
Answer:
Perimeter of the triangle is 42.9 centimetre,

Explanation:
Given sides of a triangle are 12.4 centimetre, 16.8 centimetre, 13.7 centimetre, Perimeter of the triangle = 12.4 centimetre + 16.8 centimetre + 13.7 centimetre = 42.9 centimetre.
Kerala-Syllabus-6th-Standard-Maths-Solutions-Chapter-5-Decimal-Forms-20
Question 3.
A sack has 48.75 kilograms of rice in it. From this 16.5 kilograms was given to Venu and 12.48 kilograms to Thomas. How much rice is now in the sack’?
Answer:
19.77 kilograms of rice is left in the sack,

Explanation:
Total quantity of rice the sack contain = 48.75 kilograms, Quantity of rice Venu was given = 16.5 kilograms, Quantity of rice Thomas was given = 12.48 kilograms, Quantity of rice left in the sack = Total quantity of rice the sack contain – ( Quantity of rice Venu was given + Quantity of rice Thomas was given) = 48.75 kilograms – (16.5 kilograms + 12.48 kilograms) = 19.77 kilograms.
Kerala-Syllabus-6th-Standard-Maths-Solutions-Chapter-5-Decimal-Forms-22

Question 4.
Which number added to 16.254 gives 30?
Answer:
13.746,

Explanation:
The number added to 16.254 to get 30 = 30 – 16.254 = 13.746.
Kerala-Syllabus-6th-Standard-Maths-Solutions-Chapter-5-Decimal-Forms-23

Question 5.
Faisal travelled 3.75 kilometres on bicycle, 12.5 kilometres in a bus and the remaining distance on foot. He travelled 17 kilometres in all. What distance did he walk?
Answer:
Distance walked by Faisal is 0.75 kilometres,

Explanation:
Total distance travelled by Faisal = 17 kilometres, Distance travelled by Faisal on bicycle = 3.75 kilometres, Distance travelled by Faisal on bus = 12.5 kilometres, Distance walked by Faisal = Total distance travelled by Faisal – (Distance travelled by Faisal on bicycle + Distance travelled by Faisal on bus) = 17 kilometres – (3.75 kilometres + 12.5 kilometres) = 0.75 kilometres.
Kerala-Syllabus-6th-Standard-Maths-Solutions-Chapter-5-Decimal-Forms-24

Quantities of some items are written using fraction.
Onion 1\(\frac{2}{5}\) kilogram
Tomato 1\(\frac{3}{4}\) kilogram
Chilly \(\frac{1}{4}\) kilogram
How much is the total weight? Do it by writing in decimal form which way is easier?
Answer:
Total weight is 3.4 kilogram,

Explanation:
1kg = 1000 grams, \(\frac{2}{5}\) X 1000 = 400 grams = 0.4 kilogram, \(\frac{3}{4}\) X 1000 = 750 grams = 0.75 kilogram, \(\frac{1}{4}\) = 250 grams = 0.25 kilogram, Weight of onions = 1\(\frac{2}{5}\) kilogram = 1.4 kilogram, Weight of tomatoes = 1\(\frac{3}{4}\) kilogram = 1.75 kilogram, Weight of chilly = \(\frac{1}{4}\) kilogram = 0.25 kilogram,
Total weight of vegetables = 1.4 kilogram + 1.75 kilogram + 0.25 kilogram = 3.4 kilogram,
Kerala-Syllabus-6th-Standard-Maths-Solutions-Chapter-5-Decimal-Forms-28

Question 6.
Mahadevan’s home is 4 kilometre from the school. He travels 2.75 kilometre of this distance in a bus and the remaining on foot. What distance does he walk?
Answer:
Distance walked by Mahadevan is 1.25 kilometre,

Explanation:
Total distance from Mahadevan’s home to school = 4 kilometre, Distance travelled by bus = 2.75 kilometre, Distance walked = Total distance from Mahadevan’s home to school – Distance travelled by bus = 4 – 2.75 = 1.25 kilometre.
Kerala-Syllabus-6th-Standard-Maths-Solutions-Chapter-5-Decimal-Forms-25

Question 7.
Susan bought a bangle weighing 7.4 grams and a necklace weighing 10.8 grams. She bought a ring also and the total weight of all three is 20 grams. What is the weight of the ring?
Answer:
1.8 grams is the weight of the ring,

Explanation:
Total weight of three objects = 20 grams, Weight of bangle = 7.4 grams, Weight of necklace = 10.8 grams, Weight of ring = Total weight of three objects – (Weight of bangle + Weight of necklace) = 20 – (7.4 + 10.8) = 1.8 grams.
Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 26

Question 8.
From a 10.5 metre rod, an 8.05 centimetre piece is cut off. What is the length of the remaining piece?
Answer:
Length of the remaining piece is 10.4195 metre,

Explanation:
Total length of the rod = 10.5 metre, Length of piece cut off = 8.05 centimetre = 0.0805 metre ( since 1 metre = 100 centimetre), Length of remaining piece = Total length of the rod – Length of piece cut off = 10.5 – 0.0805 = 10.4195 metre.
Kerala-Syllabus-6th-Standard-Maths-Solutions-Chapter-5-Decimal-Forms-27

Question 9.
We add 10.864 and the number got by interchanging the digits in its tenth’s and thousand’s this place. What do we get? What is the difference of these two numbers?
Answer:
Sum of the given number with the interchanged number is 21.332, Difference between these two numbers is 0.396,

Explanation:
The given number = 10.864, The number obtained by interchanging the digits in its tenth’s and thousand’s place = 10.468, Sum of these numbers = 21.332,
Kerala Syllabus 6th Standard-Maths-Solutions-Chapter 5 Decimal Forms 30
Difference of these two numbers = 0.396,
Kerala Syllabus 6th Standard Maths Solutions-Chapter 5 Decimal Forms 29

Question 10.
When 12.45 is added to a number and then 8.75 subtracted, the result was 7.34. What is the original number?
Answer:
The original number is 3.64,

Explanation:
Let the original number be x, when 12.45 is added to x and then subtracted by 8.75 we get 7.34, The original number ‘x’ is 12.45 + x – 8.75 = 7.34 then x = (7.34 + 8.75) – 12.45 = 16.09 – 12.45 = 3.64, Therefore the original number is 3.64.
Kerala Syllabus 6th Standard Maths Solutions Chapter 5 Decimal Forms 31

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