Students often refer to Kerala State Syllabus SCERT Class 7 Maths Solutions and Class 7 Maths Chapter 5 Decimal Methods Questions and Answers Notes Pdf to clear their doubts.
SCERT Class 7 Maths Chapter 5 Solutions Decimal Methods
Class 7 Maths Chapter 5 Decimal Methods Questions and Answers Kerala State Syllabus
Decimal Methods Class 7 Questions and Answers Kerala Syllabus
Page 71
Question 1.
Write the following numbers as fractions.
(i) 45.6
(ii) 45.06
(iii) 45.67
(iv) 4.506
(v) 456.07
Answer:
(i) Here, the numerator is 456.
There is only one digit after the decimal point. So, the denominator is 10. Thus, the fractional form is \(\frac{456}{10}\)
(ii) Here, the numerator is 4506.
There are two digits after the decimal point. So, the denominator is 100. Thus, the fractional form is \(\frac{4506}{100}\)
(iii) 45.67 = \(\frac{4567}{100}\)
(iv) 4.506 = \(\frac{4506}{1000}\)
(v) 456.07 = \(\frac{45607}{100}\)
Page 73
Question 1.
The figure below shows a regular pentagon.
Find the perimeter of the pentagon.
Answer:
Length of a side = 2.35 m
Number of sides = 5
Perimeter = Number of sides × Length of a side
= 5 × 2.35
= 5 × \(\frac{235}{100}\)
= \(\frac{1175}{100}\)
= 11.75 metres
Question 2.
A kid needs 1.45 metres of cloth for a shirt. How many metres of cloth is needed for 4 shirts?
Answer:
Amount of cloth needed for one shirt = 1.45 m
Number of shirts = 4
The amount of cloth needed for 4 shirts.
= 4 × Amount of cloth for one shirt
= 4 × 1.45
= 4 × \(\frac{145}{100}\)
= \(\frac{580}{100}\)
= 5.80 m
Question 3.
A bag holds 4.75 kilograms of rice. How much rice can 8 such bags hold?
Answer:
Amount of rice in one bag = 4.75 kg
Amount of rice in 8 bags = 8 × amount of rice in one bag
= 8 × 4.75
= 8 × \(\frac{475}{100}\)
= \(\frac{8 \times 475}{100}\)
= \(\frac{3800}{100}\)
= 38 kg
Question 4.
A vessel full of oil was used to fill in 6 bottles. Each bottle holds 0.75 litres. How much oil was there in the vessel?
Answer:
Amount of oil in one bottle = 0.75 litres
Amount of oil in the vessel = Amount of oil in six bottles
= = 6 × amount of oil in one bottle
= 6 × 0.75
= 6 × \(\frac{75}{100}\)
= \(\frac{6 \times 75}{100}\)
= \(\frac{450}{100}\)
= 4.50 litres
Page 74
Question 1.
Find the area in square metres of a rectangle of length 6.25 metres and width 4.2 metres.
Answer:
length = 6.25 m
width = 4.2 m
Area = length × width
= 6.25 × 4.2
= \(\frac{625}{100} \times \frac{42}{10}\)
= \(\frac{26250}{1000}\)
= 26.250 square metres
Question 2.
The weight of 1 millilitre of coconut oil is 0.91 grams. What is the weight of 10.5 millilitres of coconut oil?
Answer:
Weight of 1 millilitre of coconut oil = 0.91 g
Weight of 10.5 millilitres of coconut oil
= 10.5 × Weight of 1 millilitre of coconut oil
= 10.5 × 0.91
= \(\frac{9555}{1000}\)
= 9.555 g
Question 3.
The price of 1 litre of petrol is 110.12 rupees. What is the price of 2.5 litres of petrol?
Answer:
Price of 1 litre of petrol = 110.12 rupees
Price of 2.5 litres of petrol = 2.5 × Price of 1 litre of petrol
= 2.5 × 110.12
= \(\frac{25}{10} \times \frac{11012}{100}\)
= \(\frac{275300}{1000}\)
= 275.300 rupees
Page 76
Question 1.
Given that 1234 × 56 = 69104
Answer:
(i) Find the answers to the following problems without actual multiplication.
(i) 1.234 × 56
(ii) 12.34 × 5.6
(iii)123.4 × 0.56
(iv) 1234 × 0.056
Answer:
(i) 1.234 × 56
= 69.104
(ii) 12.34 × 5.6
= 69.104
(iii) 123.4 × 0.56
= 69.104
(iv) 1234 × 0.056
= 69.104
(ii) Like this, how many products can you find which gives 6.9104?
Answer:
0.1234 × 56 = 6.9104
1.234 × 5.6 = 6.9104
12.34 × 0.56 = 6.9104
123.4 × 0.056 = 6.9104
1234 × 0.0056 = 6.9104
So, 5 products gives 6.9104
Question 2.
In the following products, how many of them give the same product as 1.234 × 5.67?
(i) 12.34 × 0.567
(ii) 1.234 × 567
(iii) 0.1234 × 5.67
(iv) 1.234 × 56.7
(v) 123.4 × 0.0567
Answer:
1.234 × 5.67 has 5 digits after the decimal point.
(i) number of digits after the decimal point in 12.34 is 2. number of digits after the decimal point in 0.567 is 3.
Thus, the number of digits after the decimal point in the product = 2 + 3
= 5
∴same.
(ii) number of digits after the decimal point in the product = 3 + 0
= 3
∴ different.
(iii)number of digits after the decimal point in the product = 4 + 2
= 6
∴ different.
(iv)number of digits after the decimal point in the product = 3 + 1
= 4
∴ different.
(v) number of digits after the decimal point in the product = 1 + 4
= 5
∴ same.
Question 3.
Find the greatest and least products from the following:
(i) 0.11 × 0.11
(ii) 1.1 × 1.1
(iii) 1.01 × 1.01
(iv) 0.101 × 1.1
(v) 10.1 × 0.101
Answer:
(i) 0.11 × 0.11 = \(\frac{11}{100} \times \frac{11}{100}\)
= \(\frac{121}{10000}\)
= 0.0121
(ii) 1.1 × 1.1 = \(\frac{11}{10} \times \frac{11}{10}\)
= \(\frac{121}{100}\)
= 1.21
(iii) 1.01 × 1.01 = \(\frac{101}{100} \times \frac{101}{100}\)
= \(\frac{10201}{10000}\)
= 0.1111
(iv) 0.101 × 1.1 = \(\frac{101}{1000} \times \frac{11}{10}\)
= \(\frac{1111}{10000}\)
= 1.0201
(v) 10.1 × 0.101 = \(\frac{101}{10} \times \frac{101}{1000}\)
= \(\frac{10201}{10000}\)
= 1.0201
Greatest value = 1.21 ⇒ greatest product = 1.1 × 1.1
Least value = 0.0121 ⇒ least product 0.11 × 0.11
Page 78
Question 1.
The perimeter of an equilateral triangle is 12.9 centimetres. What is the length of each side?
Answer:
Perimerter = 12.9 cm
Length of one side =Perimeter ÷ number of sides
= 12.9 ÷ 3
= \(\frac{129}{10} \times \frac{1}{3}\)
= \(\frac{129}{3} \times \frac{1}{10}\)
= 43 × \(\frac{1}{10}\)
= 4.3 cm
Question 2.
16.5 kilograms of rice was divided equally among 5 people. How many kilograms did each get?
Answer:
Total amount of rice = 16.5 kg
Amount of rice each gets = total rice ÷ number of people
= 16.5 ÷ 5
= \(\frac{165}{10} \times \frac{1}{5}\)
= \(\frac{165}{5} \times \frac{1}{10}\)
= 33 × \(\frac{1}{10}\)
= 3.3 kg
Question 3.
A large vessel contains 25.2 litres of coconut oil. It was used to fill 6 small vessels of the same size. How much does each small vessel contain?
Answer:
Amount of coconut oil in the large vessel = 25.2 litres
Amount of coconut oil in each of the small vessel
= oil in large vessel ÷ number of small vessels
= 25.2 ÷ 6
= \(\frac{252}{10} \times \frac{1}{6}\)
= \(\frac{252}{6} \times \frac{1}{10}\)
= 42 × \(\frac{1}{10}\)
= 4.2 litres
Question 4.
33.6 kilograms of rice was divided equally among 8 people. Sujatha divided what she got into three equal parts and gave one part to Razia. How much did Razia get?
Answer:
Total rice = 33.6 kg
Amount of rice Sujatha gets = total rice ÷ 8
= 33.6 ÷ 8
= \(\frac{336}{10} \times \frac{1}{8}\)
= \(\frac{336}{8} \times \frac{1}{10}\)
= 42 × \(\frac{1}{10}\)
= 4.2 kg
Amount of rice Razia gets = Amount of rice Sujatha gets ÷ 3
= 4.2 ÷ 3
= \(\frac{42}{10} \times \frac{1}{3}\)
= \(\frac{42}{3} \times \frac{1}{10}\)
= 14 × \(\frac{1}{10}\)
= 1.4 kg
Question 5.
We have 7407 ÷ 6 = 1234.5
Use this result to find answers to the following questions without actual division:
(i) 740.7 ÷ 6
(ii) 74.07 ÷ 6
(iii) 7.407 ÷ 6
Answer:
(i) 740.7 ÷ 6 = \(\frac{7407}{10} \times \frac{1}{6}\)
= \(\frac{7407}{6} \times \frac{1}{10}\)
= 1234.5 × \(\frac{1}{10}\)
= 123.45
OR
Here, the decimal point in the numerator is shifted one place to the left. So, the decimal point in the answer moves one place to the left.
∴ 740.7 ÷ 6 = 123.45
(ii) Here, the decimal point in the numerator is shifted two places to the left. So, the decimal point in the answer moves two places to the left.
∴ 74.07 ÷ 6 = 12.345
(iii)Here, the decimal point in the numerator is shifted two places to the left. So, the decimal point in the answer moves three places to the left.
∴ 7.407 ÷ 6 = 1.2345
Page 80
Question 1.
Find the decimal forms of the following fractions.
(i) \(\frac{3}{5}\)
Answer:
\(\frac{3}{5}=\frac{3 \times 2}{5 \times 2}=\frac{6}{10}\)
= 0.6
(ii) \(\frac{4}{5}\)
Answer:
\(\frac{4}{5}=\frac{4 \times 2}{5 \times 2}=\frac{8}{10}\)
= 0.8
(iii) \(\frac{1}{20}\)
Answer:
\(\frac{1}{20}=\frac{1 \times 5}{20 \times 5}=\frac{5}{100}\)
(iv) \(\frac{7}{8}\)
Answer:
\(\frac{7}{8}=\frac{7 \times 125}{8 \times 125}=\frac{875}{1000}\)
=0.875
Question 2.
3 litres of milk is used to fill in 8 bottles of the same size. How many litres does each bottle hold?
Answer:
Total milk = 3 litres
Number of bottles = 8.
Amount of milk in one bottle = \(\frac{\text { Total milk }}{\text { number of bottles }}\)
= \(\frac{3}{8}\)
= \(\frac{3 \times 125}{8 \times 125}\)
= \(\frac{375}{1000}\)
= 0.375 litres
Question 3.
A rope 17 metres long is cut into 25 equal pieces. What is the length of each piece in metres?
Answer:
Total length = 17 m
Number of pieces = 25
Length of each piece = \(\frac{\text { Total length }}{\text { number of pieces }}\)
= \(\frac{17}{25}\)
= \(\frac{17 \times 4}{25 \times 4}\)
= \(\frac{68}{100}\)
= 0.68 m
Question 4.
19 kilograms of rice was equally divided among 20 people. How much kilograms did each get?
Answer:
Total rice = 19 kg
Number of peoples = 20
Amount of rice each get = \(\frac{\text { Total rice }}{\text { number of people }}\)
= \(\frac{19}{20}\)
= \(\frac{19 \times 5}{20 \times 5}\)
= \(\frac{95}{100}\)
= 0.95 kg
Page – 81
Question 1.
A ribbon 14.5 centimetres long is cut into two equal pieces. What is the length of each piece in centimetres?
Answer:
Length of the ribbon = 14.5 cm
Number of pieces = 2
Length of each piece = \(\frac{1}{\text { Number of pieces }}\) × Length of the ribbon
Question 2.
What is the length of a side of a square of perimeter 20.5 metres?
Answer:
Perimeter of the square = 20.5 m
Length of a side = \(\frac{1}{4}\) × 20.5
Question 3.
The price of 6 pens is 40.50 rupees. What is the price of one pen?
Answer:
Price of 6 pens = 40.50
Price of one pen = \(\frac{1}{6}\) × 40.50
Page 82
Question 1.
A vessel contains 4.05 litres of coconut oil. It is to be used to fill 0.45 litre bottles. How many bottles are needed?
Answer:
Total oil = 4.05 = \(\frac{405}{100}\) litres
Capacity of one bottle = 0.45 = \(\frac{45}{100}\) litres
Number of bottles =
Here, \(\frac{45}{100}\) is the dividing fraction. Its reciprocal is \(\frac{100}{45}\)
Number of bottles = \(\frac{405}{100} \times \frac{100}{45}\)
= \(\frac{405}{45}\)
= \(\frac{81 \times 5}{9 \times 5}\)
= \(\frac{81}{9}\)
= 9
Question 2.
An iron rod 17.5 metres long is cut into pieces of length 2.5 metres each. How many pieces are there?
Answer:
Length of the iron rod = 17.5 = \(\frac{175}{10}\)m
Length of one piece = 2.5 = \(\frac{25}{10}\) m
Number of pieces = \(\frac{\text { Length of the iron rod }}{\text { Length of one piece }}\)
Here, \(\frac{25}{10}\) is the dividing fraction. Its reciprocal is \(\frac{10}{25}\)
Therefore, number of pieces = \(\frac{175}{10} \times \frac{10}{25}\)
= \(\frac{175}{25}\)
= 7
Question 3.
6.5 kilograms of chilli powder was packed in 0.25 kilogram packets. How many packets are there?
Answer:
Total chilli powder = 6.5 = \(\frac{65}{10}\)kg
Amount of chilli powder in a small packet = 0.25 = \(\frac{25}{100}\) kg
Number of small packets = \(\frac{\text { Total chilli powder }}{\text { Amount of chilli powder in a small packet }}\)
Here, \(\frac{25}{100}\) is the dividing fraction. Its reciprocal is \(\frac{100}{25}\)
Therefore, the number of packets = \(\frac{65}{10} \times \frac{100}{25}\)
= \(\frac{650}{25}\)
= 26
Intext Questions And Answers
Question 1.
Write the decimal forms of the following fractions.
(i) \(\frac{325}{10}\)
Answer:
\(\frac{325}{10}\)
= 32.5
(ii) \(\frac{325}{100}\)
Answer:
\(\frac{325}{100}\)
= 3.25
(iii) \(\frac{325}{1000}\)
Answer:
\(\frac{325}{1000}\)
= 0.325
Question 2.
Complete the following table.
Express these in decimal forms also.
\(\frac{476}{10}\) =
\(\frac{476}{100}\) =
\(\frac{476}{1000}\) =
\(\frac{476}{10000}\)
Answer:
In decimal form;
\(\frac{476}{10}\)
= 47.6
\(\frac{476}{100}\)
= 4.76
\(\frac{476}{1000}\)
= 0.476
\(\frac{476}{10000}\)
= 0.0476
Question 3.
What is the fractional form of 327.045?
Answer:
Here, the numerator is 327045.
In the given decimal number,we have three digits after the decimal point. So, the denominator is 1000.
Thus, the fractional form is \(\frac{327045}{1000}\)
Class 7 Maths Chapter 5 Kerala Syllabus Decimal Methods Questions and Answers
Question 1.
What is the fraction form of 3.05?
Answer:
3.05 = \(\frac{305}{100}\)
Question 2.
\(\frac{1.234}{0.01234}\) = ?
Answer:
Question 3.
\(\frac{2.3 \times 3.2}{0.4}\) = ?
Answer:
Question 4.
\(\frac{0.013 \times 0.013}{0.0169}\) = ?
Answer:
Question 5.
If \(\frac{37}{1.5} \times \frac{1.2}{4}\) = 7.4, What is \(\frac{3.7}{0.15} \times \frac{12}{0.4}\)
Answer:
In both the cases the total number of decimal places in the numerator is same.
In the first case the total number of decimal places in the denominator is one.
In the second case the total number of decimal places in the denominator is three.
The increase in the decimal places in the denominator is two.
So, the new answer is; old answer × 100. That is,
7.4 × 100 = 740
Practice Questions
Question 1.
If the breadth of a rectangle is 2.5 metres and the area is 5.6 square metres, what is its length?
Answer:
2.24 m
Question 2.
What is the decimal form of \(\frac{3.2}{16}\)
Answer:
0.2
Question 3.
If the length of a box is 1.2 metres, breadth is 0.8 m and heigtht is 0.2 m, what is the volume of that box?
Answer:
0.192 cubic metres
Question 4.
The total weight of a box containing 5 detergent packets of the same size is the weight of each packet?
Answer:
1.68 kg
Question 5.
How many packets of \(\frac{1}{12}\) kg salt can be made from \(\frac{15}{2}\) kg of salt?
Answer:
90
Class 7 Maths Chapter 5 Notes Kerala Syllabus Decimal Methods
Decimal numbers are one of the main and commonly used concepts in mathematics. This chapter deals with some of the main ideas of decimal numbers. Following are the concepts discussed in this chapter.
Converting a fraction to a decimal
- To convert a fraction with denominator 10 and numerator a natural number to a decimal, put the decimal point just before the last digit of the numerator.
- To convert a fraction with denominator 100 and numerator a natural number to a decimal, put the decimal point just before the second last digit of the numerator.
- To convert a fraction with denominator 1000 and numerator a natural number to a decimal, put the decimal point just before the third last digit of the numerator.
In other cases, to convert a fraction with numerator a natural number to a decimal, first convert the denominator of the fraction to any of the forms 10,100, 1000, … by multiplying both the numerator and the denominator by a suitable number. Then, write the decimal form of that fraction.
Converting a decimal to a fraction
In this case, the numerator will be the given number itself (ignore the decimal point).
To write the denominator, count the number of digits after the decimal point.
If there is only one digit after the decimal point, then write 10 in the denominator.
If there are two digits after the decimal point, then write 100 in the denominator.
If there are three digits after the decimal point, then write 1000 in the denominator. And so on.
Multiplication of a decimal with a natural number
To multiply a decimal with a natural number, first convert the decimal to its fractional form and then multiply with the natural number.
Multiplication of two decimals
To multiply two decimal numbers, first of all, convert the two decimals to fractions then take their products.
The number of digits after the decimal point in the product is the sum of the number of digits after the decimal point in the numbers being multiplied.
Dividing a decimal by a natural number
To divide a decimal by a natural number, first write the decimal as a fraction and then divide it by the natural number.
Dividing two decimals
To divide two decimals, first convert both the decimals to fractions. Then, take the reciprocal of the dividing fraction. Now multiply the fractions and then write the decimal form of the resulting fraction.
(i) How to convert a fraction with denominator 10 and numerator a natural number to a decimal?
To convert a fraction with denominator 10 to a decimal, put the decimal point just before the last digit of the numerator.
Eg:
\(\frac{157}{10}\) = 15.7
\(\frac{15}{10}\) = 1.5
\(\frac{5}{10}\) = 0.5
(ii) How to convert a fraction with denominator 100 and numerator a natural number to a decimal?
To convert a fraction with denominator 100 to a decimal, put the decimal point just before the second last digit of the numerator.
Eg:
\(\frac{482}{100}\) = 4.82, \(\frac{48}{100}\) = 0.48, \(\frac{4}{100}\) = 0.04
(iii) How to convert a fraction with denominator 1000 and numerator a natural number to a decimal?
To convert a fraction with denominator 1000 to a decimal, put the decimal point just before the third last digit of the numerator.
Eg:
\(\frac{690}{1000}\) = 0.690, \(\frac{69}{1000}\) = 0.069, \(\frac{6}{1000}\) = 0.006
What is the reason for the change in the position of the decimal point when we divide a number each time by 10?
It is because each time we divide a number by 10 (or multiply by the places shift one place to the right. As a result, the decimal point moves one point to the left when we divide a number each time by 10.
Eg:
Consider the number 498. According to the place value, this number can be written as follows:
How to convert a decimal to a fraction?
The numerator will be the given number without the decimal point.
To write the denominator, count the number of digits after the decimal point.
If there is only one digit after the decimal point, then write 10 in the denominator.
If there are two digits after the decimal point, then write 100 in the denominator.
If there are three digits after the decimal point, then write 1000 in the denominator. And so on.
Multiples
How to multiply a decimal with a natural number?
To multiply a decimal with a natural number, first convert the decimal to its fractional form and then multiply with the natural number.
Eg:
5 × 1.35 = 5 × \(\frac{135}{100}\)
= \(\frac{675}{100}\)
= 6.75
Decimal Multiplication
How to multiply two decimal numbers?
First of all, convert the two decimals to fractions then take their products. Then write the decimal form of this product.
Eg:
0.15 × 3.2 = \(\frac{15}{100} \times \frac{32}{10}\)
= \(=\frac{15 \times 32}{100 \times 10}\)
= \(\frac{480}{1000}\)
= 0.480
Multiplication Operations
The number of digits after the decimal point in the product is the sum of the number of digits after the decimal point in the numbers being multiplied.
OR
The number of decimal places in the product is equal to the sum of the decimal places in the numbers being multiplied.
Eg:
We can find that 3.14 × 1.2 = 3.768
Here,
number of digits after the decimal point in 3.14 is 2.
number of digits after the decimal point in 1.2 is 1.
number of digits after the decimal point in the product 3.768
= 3
= 2 + 1
= number of digits after the decimal point in 3.14
+ number of digits after the decimal point in 1.2
The number of digits after the decimal point is exactly same as the number of zeroes in the denominator of the fractional form. (Only if the denominator is 10, 100, 1000, …)
Eg:
Parts
How to divide a decimal by a natural number?
To divide a decimal by a natural number, first write the decimal as a fraction and then divide it by the natural number. Then write the decimal form of the result.
Example 1:
10.2 ÷ 2 = \(\frac{102}{10}\) ÷ 2
= \(\frac{102}{10} \times \frac{1}{2}\)
= \(\frac{102}{2} \times \frac{1}{10}\)
= 51 × \(\frac{1}{10}\)
= 5.1
Example 2:
23.2 ÷ 4 = \(\frac{1}{4}\) × 23.2
= \(\frac{1}{4} \times \frac{232}{10}\)
= \(\frac{232}{40}\)
= \(\frac{58 \times 4}{10 \times 4}\)
= \(\frac{58}{10}\)
= 5.8
Fraction And Decimal
We get various forms of a fraction by multiplying the numerator and the denominator by the same number.
Eg:
Consider the fraction \(\frac{1}{2}\)
When we multiply both the numerator and the denominator by 5 it becomes;
\(\frac{1}{2}=\frac{1 \times 5}{2 \times 5}=\frac{5}{10}\)
When we multiply both the numerator and the denominator by 8 it becomes;
\(\frac{1}{2}=\frac{1 \times 8}{2 \times 8}=\frac{8}{16}\)
Thus, \(\frac{5}{10}\) and \(\frac{8}{16}\) are different forms of the fraction \(\frac{1}{2}\)
How to convert a fraction to a decimal?
To convert a fraction to a decimal, first convert the denominator of the fraction to any of the forms 10, 100, 1000, by multiplying both the numerator and the denominator by a suitable number. Then, write the decimal form of that fraction.
Eg:
Decimal form of \(\frac{1}{4}=\frac{1 \times 25}{4 \times 25}=\frac{25}{100}\) = 0.25
Decimal form of \(\frac{1}{8}=\frac{1 \times 125}{8 \times 125}=\frac{125}{1000}\) = 0.125
Decimal Division
How to divide two decimals?
To divide two decimals first convert both the decimals to fractions. Then take the reciprocal of the dividing fraction. Now multiply the fractions and then write the decimal form of the resulting fraction.
Eg:
3.25 ÷ 2.5 ?
3.25 =
2.5 =
Dividing fraction is \(\frac{25}{10}\).Its reciprocal is \(\frac{10}{25}\)
3.25 ÷ 2.5 = \(\frac{325}{100} \times \frac{10}{25}\)
= \(\frac{325}{10} \times \frac{1}{25}\)
= \(\frac{325}{10} \times \frac{4}{100}\)
= \(\frac{1300}{1000}\)
= 1.300