Selina Textbook Solutions: Decimal Fractions | Mathematics Class 6 ICSE PDF Download

 Page 1


IMPORTANT POINTS 
Decimal Fraction : A fraction, whose denominator is 10 or a higher power of 10 e.g. 
100, 1,000, 10,000 etc. is known as decimal fraction. 
Number of Decimal Places: The number of digits in the decimal part of a number is 
the number of decimal places in it. 
When the given number has only decimal part in it. It is always written 0 before it as 0.7, 
0.55 are written as 0.7, 0.55. 
Conversion of a Fraction into a Decimal Fraction : 
1. When the denominator is 10,100,1000, 10,000 etc. : Counting from right to left of 
the numerator of the given fraction, mark the decimal point after as many digits as 
the number of zeroes in it denominator 
 
2. When the denominator is not, 10, 100, 1000, 10,000 etc. 
Multiply both, the numerator and denominator of the given fraction, by a suitable 
number to get the denominator 10 or a power of 10 and then proceed as above, 
e.g. 
 
3. Conversion of a given Decimal Fraction into a Non-Decimal Fraction : Remove the 
decimal point and at the same time write 1 in the denominator, as many zeroes to 
the right of 1 as there are digits in the decimal part e.g., 
 
Zero or zeores written at the right of a decimal number does not change its value, 
e.g. 3.4 is the same as 3.40, 3.400, 3.4000 etc. 
EXERCISE 15(A) 
Question 1. 
Write the number of decimal places in each of the following : 
(i) 7.03 
(ii) 0.509 
(iii) 146.2 
Page 2


IMPORTANT POINTS 
Decimal Fraction : A fraction, whose denominator is 10 or a higher power of 10 e.g. 
100, 1,000, 10,000 etc. is known as decimal fraction. 
Number of Decimal Places: The number of digits in the decimal part of a number is 
the number of decimal places in it. 
When the given number has only decimal part in it. It is always written 0 before it as 0.7, 
0.55 are written as 0.7, 0.55. 
Conversion of a Fraction into a Decimal Fraction : 
1. When the denominator is 10,100,1000, 10,000 etc. : Counting from right to left of 
the numerator of the given fraction, mark the decimal point after as many digits as 
the number of zeroes in it denominator 
 
2. When the denominator is not, 10, 100, 1000, 10,000 etc. 
Multiply both, the numerator and denominator of the given fraction, by a suitable 
number to get the denominator 10 or a power of 10 and then proceed as above, 
e.g. 
 
3. Conversion of a given Decimal Fraction into a Non-Decimal Fraction : Remove the 
decimal point and at the same time write 1 in the denominator, as many zeroes to 
the right of 1 as there are digits in the decimal part e.g., 
 
Zero or zeores written at the right of a decimal number does not change its value, 
e.g. 3.4 is the same as 3.40, 3.400, 3.4000 etc. 
EXERCISE 15(A) 
Question 1. 
Write the number of decimal places in each of the following : 
(i) 7.03 
(ii) 0.509 
(iii) 146.2 
(iv) 0.0065 
(v) 8.03207 
Solution: 
(i) 7.03, the decimal part is .03 which contains two digits. 
Number 7.03 has 2 decimal places. 
(ii) 0.509, the decimal part is 0.509 which contains three digits. 
Number 0.509 has 3 decimal places 
(iii) 146.2, the decimal part is .2 which contains one digits. 
Number 146.2 has 1 decimal places. 
(iv) 0.0065, the decimal part is .0065 which contains four digits. 
Number 0.0065 has 4 decimal places 
(v) 8.03207, the decimal part is .03207 which contains five digits. 
Number 8.03207 has 5 decimal places. 
Question 2. 
Convert the given unlike decimal fractions into like decimal fractions: 
(i) 1.36, 239.8 and 47.008 
(ii) 507.0752, 8.52073 and 0.808 
(iii) 459.22, 7.03093 and 0.200037 
Solution: 
(i) 1.36 = 1.360 
239:8 = 239.800 
47.008 = 47.008 
(ii) 507.0752 = 507.07520 
8.52073 = 8.52073 
0.808 = 0.80800 
(iii) 459.22 = 459.220000 
7.03093 = 7.030930 
0.200037 = 0.200037 
Question 3. 
Change each of following fractions to a decimal fraction : 
 
Page 3


IMPORTANT POINTS 
Decimal Fraction : A fraction, whose denominator is 10 or a higher power of 10 e.g. 
100, 1,000, 10,000 etc. is known as decimal fraction. 
Number of Decimal Places: The number of digits in the decimal part of a number is 
the number of decimal places in it. 
When the given number has only decimal part in it. It is always written 0 before it as 0.7, 
0.55 are written as 0.7, 0.55. 
Conversion of a Fraction into a Decimal Fraction : 
1. When the denominator is 10,100,1000, 10,000 etc. : Counting from right to left of 
the numerator of the given fraction, mark the decimal point after as many digits as 
the number of zeroes in it denominator 
 
2. When the denominator is not, 10, 100, 1000, 10,000 etc. 
Multiply both, the numerator and denominator of the given fraction, by a suitable 
number to get the denominator 10 or a power of 10 and then proceed as above, 
e.g. 
 
3. Conversion of a given Decimal Fraction into a Non-Decimal Fraction : Remove the 
decimal point and at the same time write 1 in the denominator, as many zeroes to 
the right of 1 as there are digits in the decimal part e.g., 
 
Zero or zeores written at the right of a decimal number does not change its value, 
e.g. 3.4 is the same as 3.40, 3.400, 3.4000 etc. 
EXERCISE 15(A) 
Question 1. 
Write the number of decimal places in each of the following : 
(i) 7.03 
(ii) 0.509 
(iii) 146.2 
(iv) 0.0065 
(v) 8.03207 
Solution: 
(i) 7.03, the decimal part is .03 which contains two digits. 
Number 7.03 has 2 decimal places. 
(ii) 0.509, the decimal part is 0.509 which contains three digits. 
Number 0.509 has 3 decimal places 
(iii) 146.2, the decimal part is .2 which contains one digits. 
Number 146.2 has 1 decimal places. 
(iv) 0.0065, the decimal part is .0065 which contains four digits. 
Number 0.0065 has 4 decimal places 
(v) 8.03207, the decimal part is .03207 which contains five digits. 
Number 8.03207 has 5 decimal places. 
Question 2. 
Convert the given unlike decimal fractions into like decimal fractions: 
(i) 1.36, 239.8 and 47.008 
(ii) 507.0752, 8.52073 and 0.808 
(iii) 459.22, 7.03093 and 0.200037 
Solution: 
(i) 1.36 = 1.360 
239:8 = 239.800 
47.008 = 47.008 
(ii) 507.0752 = 507.07520 
8.52073 = 8.52073 
0.808 = 0.80800 
(iii) 459.22 = 459.220000 
7.03093 = 7.030930 
0.200037 = 0.200037 
Question 3. 
Change each of following fractions to a decimal fraction : 
 
Solution: 
 
Question 4. 
Convert into a decimal fraction : 
 
Solution: 
 
 
Question 5. 
Change the given decimals fractions to fractions in their lowest terms : 
(i) 0.05 
(ii) 3.95 
(iii) 4.005 
(iv) 0.876 
(v) 50.06 
(vi) 0.01075 
(vii) 4.8806 
Page 4


IMPORTANT POINTS 
Decimal Fraction : A fraction, whose denominator is 10 or a higher power of 10 e.g. 
100, 1,000, 10,000 etc. is known as decimal fraction. 
Number of Decimal Places: The number of digits in the decimal part of a number is 
the number of decimal places in it. 
When the given number has only decimal part in it. It is always written 0 before it as 0.7, 
0.55 are written as 0.7, 0.55. 
Conversion of a Fraction into a Decimal Fraction : 
1. When the denominator is 10,100,1000, 10,000 etc. : Counting from right to left of 
the numerator of the given fraction, mark the decimal point after as many digits as 
the number of zeroes in it denominator 
 
2. When the denominator is not, 10, 100, 1000, 10,000 etc. 
Multiply both, the numerator and denominator of the given fraction, by a suitable 
number to get the denominator 10 or a power of 10 and then proceed as above, 
e.g. 
 
3. Conversion of a given Decimal Fraction into a Non-Decimal Fraction : Remove the 
decimal point and at the same time write 1 in the denominator, as many zeroes to 
the right of 1 as there are digits in the decimal part e.g., 
 
Zero or zeores written at the right of a decimal number does not change its value, 
e.g. 3.4 is the same as 3.40, 3.400, 3.4000 etc. 
EXERCISE 15(A) 
Question 1. 
Write the number of decimal places in each of the following : 
(i) 7.03 
(ii) 0.509 
(iii) 146.2 
(iv) 0.0065 
(v) 8.03207 
Solution: 
(i) 7.03, the decimal part is .03 which contains two digits. 
Number 7.03 has 2 decimal places. 
(ii) 0.509, the decimal part is 0.509 which contains three digits. 
Number 0.509 has 3 decimal places 
(iii) 146.2, the decimal part is .2 which contains one digits. 
Number 146.2 has 1 decimal places. 
(iv) 0.0065, the decimal part is .0065 which contains four digits. 
Number 0.0065 has 4 decimal places 
(v) 8.03207, the decimal part is .03207 which contains five digits. 
Number 8.03207 has 5 decimal places. 
Question 2. 
Convert the given unlike decimal fractions into like decimal fractions: 
(i) 1.36, 239.8 and 47.008 
(ii) 507.0752, 8.52073 and 0.808 
(iii) 459.22, 7.03093 and 0.200037 
Solution: 
(i) 1.36 = 1.360 
239:8 = 239.800 
47.008 = 47.008 
(ii) 507.0752 = 507.07520 
8.52073 = 8.52073 
0.808 = 0.80800 
(iii) 459.22 = 459.220000 
7.03093 = 7.030930 
0.200037 = 0.200037 
Question 3. 
Change each of following fractions to a decimal fraction : 
 
Solution: 
 
Question 4. 
Convert into a decimal fraction : 
 
Solution: 
 
 
Question 5. 
Change the given decimals fractions to fractions in their lowest terms : 
(i) 0.05 
(ii) 3.95 
(iii) 4.005 
(iv) 0.876 
(v) 50.06 
(vi) 0.01075 
(vii) 4.8806 
Solution: 
 
EXERCISE 15(B) 
Question 1. 
Add the following : 
(i) 0.243, 2.47 and 3.009 
(ii) 0.0736, 0.6095 and 0.9107 
(iii) 1.01, 257 and 0.200 
(iv) 18, 200.35, 11.72 and 2.3 
(v) 0.586, 0.0586 and 0.00586 
Solution: 
 
 
Page 5


IMPORTANT POINTS 
Decimal Fraction : A fraction, whose denominator is 10 or a higher power of 10 e.g. 
100, 1,000, 10,000 etc. is known as decimal fraction. 
Number of Decimal Places: The number of digits in the decimal part of a number is 
the number of decimal places in it. 
When the given number has only decimal part in it. It is always written 0 before it as 0.7, 
0.55 are written as 0.7, 0.55. 
Conversion of a Fraction into a Decimal Fraction : 
1. When the denominator is 10,100,1000, 10,000 etc. : Counting from right to left of 
the numerator of the given fraction, mark the decimal point after as many digits as 
the number of zeroes in it denominator 
 
2. When the denominator is not, 10, 100, 1000, 10,000 etc. 
Multiply both, the numerator and denominator of the given fraction, by a suitable 
number to get the denominator 10 or a power of 10 and then proceed as above, 
e.g. 
 
3. Conversion of a given Decimal Fraction into a Non-Decimal Fraction : Remove the 
decimal point and at the same time write 1 in the denominator, as many zeroes to 
the right of 1 as there are digits in the decimal part e.g., 
 
Zero or zeores written at the right of a decimal number does not change its value, 
e.g. 3.4 is the same as 3.40, 3.400, 3.4000 etc. 
EXERCISE 15(A) 
Question 1. 
Write the number of decimal places in each of the following : 
(i) 7.03 
(ii) 0.509 
(iii) 146.2 
(iv) 0.0065 
(v) 8.03207 
Solution: 
(i) 7.03, the decimal part is .03 which contains two digits. 
Number 7.03 has 2 decimal places. 
(ii) 0.509, the decimal part is 0.509 which contains three digits. 
Number 0.509 has 3 decimal places 
(iii) 146.2, the decimal part is .2 which contains one digits. 
Number 146.2 has 1 decimal places. 
(iv) 0.0065, the decimal part is .0065 which contains four digits. 
Number 0.0065 has 4 decimal places 
(v) 8.03207, the decimal part is .03207 which contains five digits. 
Number 8.03207 has 5 decimal places. 
Question 2. 
Convert the given unlike decimal fractions into like decimal fractions: 
(i) 1.36, 239.8 and 47.008 
(ii) 507.0752, 8.52073 and 0.808 
(iii) 459.22, 7.03093 and 0.200037 
Solution: 
(i) 1.36 = 1.360 
239:8 = 239.800 
47.008 = 47.008 
(ii) 507.0752 = 507.07520 
8.52073 = 8.52073 
0.808 = 0.80800 
(iii) 459.22 = 459.220000 
7.03093 = 7.030930 
0.200037 = 0.200037 
Question 3. 
Change each of following fractions to a decimal fraction : 
 
Solution: 
 
Question 4. 
Convert into a decimal fraction : 
 
Solution: 
 
 
Question 5. 
Change the given decimals fractions to fractions in their lowest terms : 
(i) 0.05 
(ii) 3.95 
(iii) 4.005 
(iv) 0.876 
(v) 50.06 
(vi) 0.01075 
(vii) 4.8806 
Solution: 
 
EXERCISE 15(B) 
Question 1. 
Add the following : 
(i) 0.243, 2.47 and 3.009 
(ii) 0.0736, 0.6095 and 0.9107 
(iii) 1.01, 257 and 0.200 
(iv) 18, 200.35, 11.72 and 2.3 
(v) 0.586, 0.0586 and 0.00586 
Solution: 
 
 
Question 2. 
Find the value of : 
(i) 6.8 – 2.64 
(ii) 2 – 1.0304 
(iii) 0.1 – 0.08 
(iv) 0.83 – 0.342 
Solution: 
 
Question 3. 
Subtract : 
(i) 0.43 from 0.97 
(ii) 2.008 from 22.1058 
(iii) 0.18 from 0.6 
(iv) 1.002 from 17 
(v) 83 from 92.05 
Solution: