Students often refer to Kerala State Syllabus SCERT Class 6 Maths Solutions and Class 6 Maths Chapter 5 Decimal Forms Questions and Answers Notes Pdf to clear their doubts.
SCERT Class 6 Maths Chapter 5 Solutions Decimal Forms
Class 6 Kerala Syllabus Maths Solutions Chapter 5 Decimal Forms Questions and Answers
Decimal Forms Class 6 Questions and Answers Kerala Syllabus
Decimal Places (Page No. 69)
Question 1.
Split the numbers below according to place value:
(i) 4.5
(ii) 4.57
(iii) 4.572
(iv) 45.72
(v) 457.2
Answer:
Textbook Page No. 71
Question 1.
Now try to write 4 kilograms and 55 grams as kilograms in decimal form.
Answer:
4 kilograms 55 grams
55 grams means \(\frac {55}{1000}\) kilograms.
So, 4 kilograms 55 grams = 4\(\frac {55}{1000}\) kilograms
Splitting 4\(\frac {55}{1000}\) according to place value
So we can write the decimal form of 4\(\frac {55}{1000}\) as 4.055
Question 2.
Convert the measures below into the measures specified, using fractions and decimal forms.
Answer:
Decimals and Fractions (Page No. 74)
Question 1.
The decimal form of some numbers is given below. Write each of them as a fraction with a denominator of 10, 100, or 1000.
(i) 3.7
(ii) 3.07
(iii) 30.7
(iv) 3.72
(v) 37.2
(vi) 3.072
(vii) 30.72
Answer:
(i) \(\frac {37}{10}\)
(ii) \(\frac {307}{100}\)
(iii) \(\frac {307}{10}\)
(iv) \(\frac {372}{100}\)
(v) \(\frac {372}{10}\)
(vi) \(\frac {3072}{1000}\)
(vii) \(\frac {3072}{100}\)
Question 2.
Write the decimal form of the fractions given below.
(i) \(\frac {51}{100}\)
(ii) \(\frac {513}{10}\)
(iii) \(\frac {513}{100}\)
(iv) \(\frac {513}{1000}\)
(v) \(\frac {5130}{1000}\)
Answer:
(i) 5.1
(ii) 51.3
(iii) 5.13
(iv) 0.513
(v) 5.13
Addition and Subtraction (Page No. 79)
Question 1.
Anu made an 8.5 metre long festoon and Sarah made a 7.8 metre long one to decorate their classroom for the school anniversary. What is the total length of the festoon they made?
Answer:
Length of the festoon Anu made = 8.5 metres
Length of the Festoon Sarah made = 7.8 metres
Removing the measures and converting into a fraction
8.5 = \(\frac {85}{10}\)
7.8 = \(\frac {78}{10}\)
Adding the fraction
\(\frac{85}{10}+\frac{78}{10}=\frac{163}{10}\)
Converting to decimals
\(\frac {163}{10}\) = 16.3
Total length of the festoon = 16.3 metres
Question 2.
Amal needs 2.25 metres of cloth and Sagar, 1.85 metres for a school uniform. How many metres of cloth in all?
Answer:
Length of the cloth Amal needs for the school uniform = 2.25 metres
Length of the cloth Sagar needs for the school uniform = 1.85 metres
Removing measures and converting to fractions
2.25 = \(\frac {225}{100}\)
1.85 = \(\frac {185}{100}\)
Adding these fractions
\(\frac{225}{100}+\frac{185}{100}=\frac{200+100+25+85}{100}=\frac{410}{100}\)
Converting this to decimals \(\frac {410}{100}\) = 4.1
Total length of cloth in all is 4.1 metres.
Question 3.
A tin weighs 2.85 kilograms, and it is filled with 12.5 kilograms of rice. What is the total weight?
Answer:
Weight of the tin = 2.85 kilograms
Amount of rice filled in the tin = 12.5 kilograms
Removing measures and converting to fractions
2.85 = \(\frac {285}{100}\)
12.5 = \(\frac {125}{10}\)
Adding these fractions
\(\frac{285}{100}+\frac{125}{10}\)
To add these changing \(\frac {125}{10}\) to a form with denominator
\(\frac{125 \times 10}{10 \times 10}=\frac{1250}{100}\)
Adding these fractions,
\(\frac{1250}{100}+\frac{285}{100}\)
1000 + 200 + 250 + 85 = 1200 + 335 = 1535
\(\frac{1250}{100}+\frac{285}{100}=\frac{1535}{100}\)
Converting the fractions to decimals
\(\frac {1535}{100}\) = 15.35
Total weight = 15.35 kilograms
Question 4.
Bakul walks 2.25 kilometres in the morning and 1.5 kilometres in the evening every day. What is the total distance she walks each day?
Answer:
Distance Bakul walks in the morning = 2.25 kilometres
Distance Bakul walks in the evening = 1.5 kilometres
Total distance she walks each day = 2.25 kilometres + 1.5 kilometres
Removing measures and converting to fractions
2.25 = \(\frac {225}{100}\)
1.5 = \(\frac {15}{10}\)
To add these, change \(\frac {15}{10}\) to a form with denominator 100
\(\frac{15 \times 10}{10 \times 10}=\frac{150}{100}\)
Adding the fractions
\(\frac{225}{100}+\frac{150}{100}\)
200 + 100 + 25 + 50 = 375
\(\frac{225}{100}+\frac{150}{100}=\frac{375}{100}\)
Converting the fractions to decimals
\(\frac {375}{100}\) = 3.75
Total distance she walks each day = 3.75 kilometres
Question 5.
Two small bottles contain 0.850 litres and 0.375 litres of honey. If both the bottles are emptied into a large bottle, how much honey does it contain?
Answer:
Amount of honey in the first bottle = 0.850 litres
Amount of honey in the second bottle = 0.375 litres
Amount of honey in the large bottle = 0.850 litre + 0.375 litre
Removing measures and making into fractions
0.375 = \(\frac {375}{1000}\)
0.850 = \(\frac {850}{1000}\)
Adding these \(\frac{375}{1000}+\frac{850}{1000}\)
375 + 850 = 300 + 800 + 75 + 50 = 1225
\(\frac{375}{1000}+\frac{850}{1000}=\frac{1225}{1000}\)
Converting the fractions into decimals
\(\frac {1225}{1000}\) = 1.225
Amount of honey in the large bottle = 1.225 litres.
Textbook Page No. 82
Question 1.
From a rod 14.7 metres long, a piece 7.75 metres long is cut off. What is the length of the remaining piece?
Answer:
Length of the long rod = 14.7 metres
Length of the piece cut off from the long rod = 7.75 metres
Length of the remaining piece = 14.7 metre – 7.75 metres
Changing into fractions
14.7 = \(\frac {147}{10}\)
7.75 = \(\frac {775}{100}\)
To subtract change \(\frac {147}{10}\) to a form with denominator 100
\(\frac{147 \times 10}{10 \times 10}=\frac{1470}{100}\)
Subtracting \(\frac{1470}{100}-\frac{775}{100}=\frac{695}{100}\)
Changing back to decimals
\(\frac {695}{100}\) = 6.95
Length of the remaining piece = 6.95 metres.
Question 2.
There were 38.7 kilograms of rice in a sack, and 12.350 kilograms of this were used up. How much rice remains in the sack?
Answer:
Amount of rice in the sack = 38.7 kilograms
Amount of rice used up = 12.350 kilograms
Amount of rice remaining in the sack = 38.7 kilograms – 12.350 kilograms
38.7 = \(\frac {387}{10}\)
12.350 = \(\frac {12350}{1000}\)
\(\frac{387}{10}-\frac{12350}{1000}\)
\(\frac{387 \times 100}{10 \times 100}=\frac{38700}{1000}\)
Subtracting \(\frac{38700}{1000}-\frac{12350}{1000}=\frac{26350}{1000}\)
Changing back to decimals
\(\frac {26350}{1000}\) = 26.35
Amount of rice remaining in the sack = 26.35 kilograms
Question 3.
The perimeter of a rectangle is 24 centimetres and the length of one side is 6.4 centimetres. What is the length of the other side?
Answer:
Perimeter of rectangle = 2(length + breadth) = 24 centimetres
Length of one side = 6.4 centimetres
Length of the other side = 12 – 6.4 = 5.6 centimetres
Question 4.
There were 2.50 litres of oil in a bottle, and 0.475 litres of this were used for cooking. How much oil is left in the bottle?
Answer:
Amount of oil in the bottle = 2.50 litres
Amount of oil used for cooking = 0.475 litres
Amount of oil left in the bottle = 2.50 litres – 0.475 litres
2.50 = \(\frac {250}{100}\)
0.475 = \(\frac {475}{1000}\)
\(\frac{250}{100}-\frac{475}{1000}\)
\(\frac{250 \times 10}{100 \times 10}=\frac{2500}{1000}\)
Subtracting \(\frac{2500}{1000}-\frac{475}{1000}=\frac{2025}{1000}\)
Amount of oil remaining = 2.025 litres
Question 5.
What number must we add to 14.32 to get 16.43?
Answer:
Number to be added to 14.32 to get 16.43 = 16.43 – 14.32
16.43 = \(\frac {1643}{100}\)
14.32 = \(\frac {1432}{100}\)
Subtracting \(\frac{1643}{100}-\frac{1432}{100}=\frac{211}{100}\)
Converting back to decimals
\(\frac {211}{100}\) = 2.11
Class 6 Maths Chapter 5 Kerala Syllabus Decimal Forms Questions and Answers
Class 6 Maths Decimal Forms Questions and Answers
Question 1.
Split the numbers below according to place value.
(i) 3.6
(ii) 3.64
(iii) 3.641
(iv) 36.41
(v) 364.1
Answer:
Question 2.
Convert the following measures into the specified forms, using both fractions and decimal forms.
Answer:
Question 3.
The decimal form of some numbers is given below. Write each of them as a fraction with a denominator of 10, 100, or 1000.
(i) 4.2
(ii) 4.02
(iii) 40.2
(iv) 4.25
(v) 42.5
(vi) 4.025
(vii) 40.25
Answer:
(i) \(\frac {42}{10}\)
(ii) \(\frac {402}{100}\)
(iii) \(\frac {402}{10}\)
(iv) \(\frac {425}{100}\)
(v) \(\frac {4025}{1000}\)
(vi) \(\frac {4025}{100}\)
Question 4.
Write the decimal form of the fractions given below.
(i) \(\frac {9}{10}\)
(ii) \(\frac {47}{100}\)
(iii) \(\frac {381}{1000}\)
(iv) \(\frac {15}{10}\)
(v) \(\frac {245}{100}\)
(vi) \(\frac {7}{100}\)
(vii) \(\frac {82}{1000}\)
(viii) \(\frac {3456}{1000}\)
Answer:
(i) 0.9
(ii) 0.47
(iii) 0.381
(iv) 1.5
(v) 2.45
(vi) 0.07
(vii) 0.082
(viii) 3.456
Question 5.
John ran a distance of 4.25 kilometres and then walked another 2.5 kilometres. What is the total distance he covered?
Answer:
Distance John ran = 4.25 kilometres
Distance he walked = 2.5 kilometres
Total distance he covered = 4.25 kilometres + 2.5 kilometres
Converting into fractions
4.25 = \(\frac {425}{100}\)
25 = \(\frac{25}{10}=\frac{25 \times 10}{10 \times 10}=\frac{250}{100}\)
Adding \(\frac{425}{100}+\frac{250}{100}=\frac{675}{100}\)
Converting to decimals
\(\frac {675}{100}\) = 6.75
Total distance John covered = 6.75 kilometres
Question 6.
A baker has two bags of flour, one with 1.75 kilograms of flour and the other with 2.5 kilograms. If the baker combines all the flour into a single container, what is the total weight of the flour in the container?
Answer:
Total weight of the flour in the container = Amount of flour in Bag 1 + Amount of flour in Bag 2 = 1.75 kilograms + 2.5 kilograms
1.75 = \(\frac {175}{100}\)
2.5 = \(\frac{25}{10}=\frac{25 \times 10}{10 \times 10}=\frac{250}{100}\)
Adding \(\frac{175}{100}+\frac{250}{100}=\frac{425}{100}\)
Converting into decimals
\(\frac {425}{100}\) = 4.25
Total weight of the flour in the container = 4.25 kilograms
Question 7.
A ribbon was 15.8 metres long. If a piece measuring 4.25 metres was cut from it, how much ribbon is left?
Answer:
Length of the ribbon = 15.8 metres
Length of the piece cut off from the ribbon = 4.25 metres
Length of the ribbon left = 15.8 metres – 4.25 metres
15.8 = \(\frac{158}{10}=\frac{158 \times 10}{10 \times 10}=\frac{1580}{100}\)
4.25 = \(\frac {425}{100}\)
Subtracting \(\frac{1580}{100}-\frac{425}{100}=\frac{1155}{100}\)
Converting back to decimals
\(\frac {1155}{100}\) = 11.55
Length of the ribbon left = 11.55 metres
Question 8.
A water tank holds 50.5 litres of water. If 25.5 litres are used for gardening, how much water is left in the tank?
Answer:
Amount of water left in the tank = Amount of water that the water tank can hold – Amount of water used for gardening
50.5 = \(\frac {505}{10}\)
255 = \(\frac {255}{10}\)
Subtracting \(\frac{505}{10}-\frac{255}{10}=\frac{250}{10}\)
Converting to decimals
\(\frac {250}{10}\) = 2.5
Question 9.
A carpenter uses a 2.75-metre board and a 1.5-metre board for a project. What is the total length of the wood used?
Answer:
Total length of the wood used = 2.75 metre + 1.5 metre
2.75 = \(\frac {275}{100}\)
1.5 = \(\frac{15}{10}=\frac{15 \times 10}{10 \times 10}=\frac{150}{100}\)
Adding \(\frac{275}{100}+\frac{150}{100}=\frac{425}{100}\)
Converting to decimals
\(\frac {425}{100}\) = 4.25
Total length of the wood used = 4.25 metres
Question 10.
A plant is 15.6 centimetres tall. How many more centimetres must it grow to reach a height of 20.1 centimetres?
Answer:
Height of the plant = 15.6 centimetres
Target height = 20.1 centimetres
Height the plant must grow = 20.1 centimetres – 15.6 centimetres
20.1 = \(\frac {201}{10}\)
15.6 = \(\frac {156}{10}\)
Subtracting \(\frac{201}{10}-\frac{156}{10}=\frac{45}{10}\)
Converting to decimals
\(\frac {45}{10}\) = 4.5
The plant must grow 4.5 centimetres to reach the target height.
Class 6 Maths Chapter 5 Notes Kerala Syllabus Decimal Forms
→ In the decimal form of a number, the dot (decimal point) separates the whole number part and the fractional part.
→ Digits to the left of the decimal point represent ones, tens, hundreds, and so on;
→ The digits to the right represent tenths, hundredths, thousandths, and so on.
→ Decimals allow us to represent quantities that are not whole numbers with greater precision, making them essential for measurements, money, and other real-world applications.
→ To convert a measurement from centimetres to metres in decimal form, divide the number of centimetres by 100. This is equivalent to moving the decimal point two places to the left.
→ If you have a combination of metres and centimetres, first convert the centimetres to metres as a decimal and then add them to the whole number of metres.
→ To convert a measurement from centimetres to millimetres, multiply the number by 10.
→ To convert from millimetres to centimetres, divide the number by 10.
→ To add decimal numbers representing measurements (like 4.3 cm and 2.5 cm), align the decimal points and add them directly.
→ Alternatively, you can convert the measurements to a smaller unit (like millimetres) and complete the addition, then convert the result back to the original unit.
→ To subtract a decimal from another (like subtracting 3.2 cm from 8.5 cm), you can convert both decimals to fractions with a common denominator, subtract them, and then convert the result back into a decimal.
This chapter comprehensively covers the representation and manipulation of numbers beyond whole units. Key topics include understanding decimal places to denote fractional parts, establishing the crucial relationship and conversion techniques between decimals and fractions, and mastering the fundamental operations of addition and subtraction of decimal numbers to build foundational arithmetic skills.
Decimal Places
The length of a pencil can be said in different ways:
- 5 centimetres 7 millimetres
- 5\(\frac {7}{10}\) centimetres
- 5.7 centimetres
We can write other measures also like this:
5\(\frac {7}{10}\) litres = 5.7 litres
5\(\frac {7}{10}\) kilograms = 5.7 kilograms
We can drop all references to measures and simply say that 5.7 is the decimal form of the number 5\(\frac {7}{10}\).
5\(\frac {7}{10}\) = 5.7
Similarly, 4.29 is the decimal form of 4\(\frac {29}{100}\)
4\(\frac {29}{100}\) = 4.29
We write natural numbers using ones, tens, hundreds, and so on.
For example: 247 = 2 hundreds + 4 tens + 7 ones
Splitting 247.3
Split it as the sum of a whole number and a fraction.
247.3 = 247\(\frac {3}{10}\) = 247 + \(\frac {3}{10}\)
First, we split 247.3 as the sum of a whole number and a fraction, as
247.3 = 247\(\frac {3}{10}\) = 247 + \(\frac {3}{10}\)
The \(\frac {3}{10}\) here can be written as
\(\frac{3}{10}=\frac{1}{10}+\frac{1}{10}+\frac{1}{10}\)
That is, 3 tenths. So, we can write 247.3 in terms of hundreds, tens, ones, and tenths:
247.3 = 2 hundreds + 4 tens + 7 ones + 3 tenths
Splitting 247.39
First, we write it as
247.39 = 247\(\frac {39}{100}\)= 247 + \(\frac {39}{100}\)
Then, we can split \(\frac {39}{100}\) as
\(\frac{39}{100}=\frac{30+9}{100}=\frac{30}{100}+\frac{9}{100}=\frac{3}{10}+\frac{9}{100}\)
The \(\frac {3}{10}\) here is 3 tenths: and \(\frac {9}{100}\) is 9 hundredths.
So 247.39 = 2 hundreds + 4 tens + 7 ones + 3 tenths + 9 hundredths
In the decimal form of a number, the dot separates the whole number part and the fractional part. Digits to the left of the dot show the multiples of ones, tens, hundreds, and so on; the digits to the right show the multiples of tenths, hundredths, thousandths, and so on.
For example, the two numbers used in the above examples can be split according to place value like this:
Question 1.
What is the decimal form of 23 metres 40 centimetres?
Answer:
Method 1
23 metres 40 centimetres = 23\(\frac {40}{100}\) metres = 23.40 metres
Taking only the numbers, we have
23\(\frac {40}{100}\) = 23.40
We can write the \(\frac {40}{100}\) here as
\(\frac{40}{100}=\frac{4}{10}\)
So, we get 23\(\frac {40}{100}\) = 23\(\frac {4}{10}\) = 23.4
This means 23.40 = 23.4
Method 2
Using place value
Thus, we can write 23 metres and 40 centimetres in two different ways:
23 metres 40 centimetres = 23.40 metres
23 metres 40 centimetres = 23.4 metres
Question 2.
What is the decimal form of 23 metres 4 centimetres?
Answer:
4 centimetres = \(\frac {4}{100}\) metre.
23 metres 4 centimetres =23\(\frac {4}{100}\) metres
Split 23\(\frac {4}{100}\) according to place value:
23\(\frac {4}{100}\) = 2 tens + 3 ones + 4 hundredths
The decimal form of 23\(\frac {4}{100}\) = 23.04
Question 3.
What is the decimal form of 23 metres and 4 millimetres?
Answer:
4 millimetres means \(\frac {4}{1000}\) metres.
So 23 metres 4 millimetres = 23\(\frac {4}{1000}\) metres
Split 23\(\frac {4}{1000}\) according to place value.
So, we can write the decimal form of 23\(\frac {4}{1000}\) as
23\(\frac {4}{1000}\) = 23.004
Converting Centimetres to a Decimal Form of Metres
To convert centimetres to a decimal form of metres, first, write the number of metres as the whole number part of your decimal.
Next, express the number of centimetres as a fraction of a metre. Since there are 100 centimetres in 1 metre, the denominator of your fraction will be 100. For example, 40 centimetres would be written as \(\frac {40}{100}\) metres.
Combine the whole number and the fraction to create a mixed number, such as 23\(\frac {40}{100}\).
To get the decimal form, divide the numerator of your fraction by 100. This is the same as moving the decimal point two places to the left. So, \(\frac {40}{100}\) becomes 0.40.
Finally, add the decimal to the whole number.
For example, 23 + 0.40 = 23.40.
The result is the length in meters.
Decimals and Fractions
Conversion of decimals into fractions
Start with the decimal number you want to convert.
Example: 7.3 centimetres
Write this in millimetres
7 centimetres = 70 millimetres
To convert \(\frac {3}{10}\) centimetres into millimetres:
\(\frac {3}{10}\) is three \(\frac {1}{10}\)
\(\frac {3}{10}\) centimetres = 3 millimetres
7.3 centimetres = 70 millimetres + 3 millimetres
Converting 73 millimetres into centimetres:
Divide it by 10
73 millimetres = \(\frac {73}{10}\) centimetres
Removing measure and writing as just numbers 7.3 = \(\frac {73}{10}\)
Question 4.
How do we write 7.31 metres as a fraction?
Answer:
Write it as a whole number and a fraction
7.31 metres = 7\(\frac {31}{100}\) metres
7 metres = 700 centimetres
\(\frac {31}{100}\) metres = 31 centimetres
7.31 metres = 700 centimetres + 31 centimetres = 731 centimeters
Converting this into metres
731 centimetres = \(\frac {731}{100}\) metres
7.31 metres = \(\frac {731}{100}\) metres
Question 5.
Convert 7.319 litres as a fraction.
Answer:
7.319 litres = 7\(\frac {319}{1000}\) litres
7 litres = 7000 millilitres
\(\frac {319}{1000}\) litres = 319 millilitres
7.319 litres = 7319 millilitres
Converting back to litres
7319 millilitres = \(\frac {7319}{1000}\) litres
7.319 litres = \(\frac {7319}{1000}\) litres
Converting 12.03 to a Fraction
- Step 1: Count the digits after the decimal point in 12.03. There are two digits (0 and 3).
- Step 2: The denominator is 100 because there are two digits after the decimal.
- Step 3: Remove the decimal point from 12.03 to get the numerator, which is 1203.
- Step 4: The final fraction is \(\frac {1203}{100}\).
Question 6.
What is the decimal form of \(\frac {1203}{1000}\)?
Answer:
Looking at the denominator, we can say there will be three digits after the decimal point.
\(\frac {1203}{1000}\) = 1.203
Addition and Subtraction
Addition of Decimal Numbers
A line 4.3 centimetres long was drawn and then extended by another 2.5 centimetres:
To find the total length of the line we have to add 4.3 centimetres and 2.5 centimetres
Method 1
Convert these to centimetres and millimetres.
4.3 centimetres = 4 centimetres 3 millimetres
2.5 centimetres = 2 centimetres 5 millimetres
And add the centimetres and millimetres separately.
4 centimetres + 2 centimetres = 6 centimetres
3 millimetres + 5 millimetres = 8 millimetres
The length of the line is 6 centimetres, 8 millimetres
Convert back to centimetres.
6 centimetres 8 millimetres = \(\frac {68}{10}\) centimetres = 6.8 centimetres
Method 2
Write the lengths in millimetres.
4.3 centimetres = 43 millimetres
2.5 centimetres = 25 millimetres
Add 43 and 25
43 + 25 = 40 + 20 + 3 + 5 = 68
Thus, the length of the line is 68 millimetres
Write as centimetres in decimal form.
68 millimetres = 6 centimetres 8 millimetres = 6.8 centimetres
Method 3
Remove the measures and write the numbers as fractions.
4.3 = \(\frac {43}{10}\)
2.5 = \(\frac {25}{10}\)
And these fractions we can add like this:
\(\frac{43}{10}+\frac{25}{10}=\frac{43+25}{10}=\frac{68}{10}\)
Write the fraction as a decimal number
\(\frac {68}{10}\) = 6.8
The length of the line is 6.8 centimetres.
Question 7.
Add 4.3 centimetres and 2.8 centimetres.
Answer:
Changing the lengths into millimetres
4.3 centimetres = 43 millimetres
2.8 centimetres = 28 millimetres
Adding 43 and 28
43 + 28 = 40 + 20 + 3 + 8 = 60 + 11 = 71
Thus, the length of this line is 71 millimetres.
Write in centimetres as a decimal:
71 millimetres = 7 centimetres 1 millimetre = 7.1 centimetres
Convert the numbers to fractions
4.3 = \(\frac {43}{10}\)
2.8 = \(\frac {28}{10}\)
Add the fractions:
\(\frac{43}{10}+\frac{28}{10}=\frac{43+28}{10}=\frac{71}{10}\)
Convert the fraction back to the decimal form.
\(\frac {71}{10}\) = 7.1
The length of the line is 7.1 centimetres.
Question 8.
A jar contains 3.5 litres of oil, and 6.25 litres more is poured into it. How much oil does the jar contain now?
Answer:
Convert just the numbers to fractions:
3.5 = \(\frac {35}{10}\)
6.25 = \(\frac {625}{100}\)
We can write \(\frac {35}{10}\) also as a fraction with denominator 100:
\(\frac{35}{10}=\frac{35 \times 10}{10 \times 10}\) = \(\frac {350}{100}\)
Now we can add like this:
\(\frac{35}{10}+\frac{625}{100}=\frac{350}{100}+\frac{625}{100}=\frac{300+600+50+25}{100}\)
= \(\frac{350+625}{100}\)
= \(\frac {975}{100}\)
Amount of oil the jar contains = 9.75 litres
Question 9.
A person bought 2.5 kilograms of rice and 3.125 kilograms of vegetables. What is the total weight?
Answer:
Converting into fractions
2.5 = \(\frac {25}{10}\)
3.125 = \(\frac {3125}{1000}\)
To add these, we change \(\frac {25}{10}\) to a form with a denominator of 1000.
\(\frac{25}{10}=\frac{25 \times 100}{10 \times 100}\) = \(\frac {2500}{1000}\)
Now, we add the fractions:
\(\frac{25}{10}+\frac{3125}{1000}=\frac{2500}{1000}+\frac{3125}{1000}\) = \(\frac{2500+3125}{1000}\)
One way of adding 2500 and 3125 is this:
2500 + 3125 = 2000 + 3000 + 500 + 125 = 5000 + 625 = 5625
So, we can continue our addition of fractions:
\(\frac{25}{10}+\frac{3125}{1000}=\frac{2500+3125}{1000}\) = \(\frac {5625}{1000}\)
Converting this to decimals:
\(\frac {5625}{1000}\) = 5.625
Thus, the total weight is 5.625 kilograms.
Subtraction of Decimal Numbers
Example: From an 8.5 centimetres long eerkkil, a 3.2 centimetres long piece is broken off. What is the length of the remaining piece?
Thinking in terms of numbers alone, what we need is to subtract 3.2 from 8.5.
We change the numbers to fractions.
8.5 = \(\frac {85}{10}\)
3.2 = \(\frac {32}{10}\)
Now we can subtract:
\(\frac{85}{10}-\frac{32}{10}=\frac{85-32}{10}\)
One way to subtract 32 from 85 is this:
85 – 32 = (80 – 30) + (5 – 2) = 50 + 3 = 53
So we get \(\frac{85}{10}-\frac{32}{10}=\frac{53}{10}\)
Finally, we switch back to decimals:
\(\frac {53}{10}\) = 5.3
Thus, the length of the remaining piece of eerkkil is 5.3 centimetres.
Question 10.
From an 8.5 centimetres long eerkkil, a 3.7 centimetres long piece is broken off. What is the length of the remaining piece?
Answer:
We start as before by converting the decimals to fractions:
8.5 = \(\frac {85}{10}\)
3.7 = \(\frac {37}{10}\)
And then subtract
\(\frac{85}{10}-\frac{37}{10}=\frac{85-37}{10}\)
We have seen in earlier classes that subtraction like 85 different ways.
For example,
85 – 37 = (85 – 35) – 2 = 50 – 2 = 48
85 – 37 = (87 – 37) – 2 = 50 – 2 = 48
85 – 37 = (85 – 40) + 3 = 45 + 3 = 48
Anyway, we find
\(\frac{85}{10}-\frac{37}{10}=\frac{48}{10}\)
Changing back to decimals,
\(\frac {48}{10}\) = 4.8
The remaining piece of eerkkil is 4.8 centimetres long.
Question 11.
There are 15 kilograms of rice in a sack. 4.25 kilograms from this are put in a bag. How much rice remains in the sack?
Answer:
Thinking just in terms of numbers, what we have to do is subtract 4.25 from 15.
Write 4.25 as a fraction:
4.25 = \(\frac {425}{100}\)
Write 15 as a fraction with a denominator of 100.
15 = \(\frac{15}{1}=\frac{15 \times 100}{1 \times 100}=\frac{1500}{100}\)
Subtracting \(\frac{1500}{100}-\frac{425}{100}=\frac{1500-425}{100}\)
We can do 1500 – 425 in several ways:
1500 – 425 = 1000 + 500 – 425 = 1000 + 75 = 1075
1500 – 425 – 1425 – 425 + 75 = 1000 + 75 = 1075
1500 – 425 = 1500 – 500 + 75 = 1000 + 75 = 1075
Thus, we have:
\(\frac{1500}{100}-\frac{425}{100}=\frac{1075}{100}\)
Changing back to decimals:
\(\frac {1075}{100}\) = 10.75
So, there are 10.75 kilograms of rice still in the sack.