Decimal Fractions — Exercise 7(A)

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

Answer

(i) In 7.03, the decimal part is .03, which contains two digits.

Hence, 7.03 has 2 decimal places.

(ii) In 0.509, the decimal part is .509, which contains three digits.

Hence, 0.509 has 3 decimal places.

(iii) In 146.2, the decimal part is .2, which contains one digit.

Hence, 146.2 has 1 decimal place.

(iv) In 0.0065, the decimal part is .0065, which contains four digits.

Hence, 0.0065 has 4 decimal places.

(v) In 8.03207, the decimal part is .03207, which contains five digits.

Hence, 8.03207 has 5 decimal places.

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

Answer

To make decimal fractions like, we make the number of decimal places equal by putting the required number of zeroes on the extreme right of the decimal part.

(i) The maximum number of decimal places is 3, so we make each number have 3 decimal places.

1.360, 239.800 and 47.008

(ii) The maximum number of decimal places is 5, so we make each number have 5 decimal places.

507.07520, 8.52073 and 0.80800

(iii) The maximum number of decimal places is 6, so we make each number have 6 decimal places.

459.220000, 7.030930 and 0.200037

Change each of following fractions to a decimal fraction:

(i) $\dfrac{7}{10}$

(ii) $\dfrac{47}{10}$

(iii) $\dfrac{343}{100}$

(iv) $\dfrac{3}{10^3}$

(v) $\dfrac{7295}{10^5}$

(vi) $\dfrac{289}{10^6}$

(vii) Ninety five-hundredths

Answer

Count the number of zeroes in the denominator of the given fraction and mark the decimal point in the numerator, after as many digits from the right as there are zeroes in the denominator.

(i) $\dfrac{7}{10}$ = 0.7

(ii) $\dfrac{47}{10}$ = 4.7

(iii) $\dfrac{343}{100}$ = 3.43

(iv) $\dfrac{3}{10^3} = \dfrac{3}{1000}$ = 0.003

(v) $\dfrac{7295}{10^5} = \dfrac{7295}{100000}$ = 0.07295

(vi) $\dfrac{289}{10^6} = \dfrac{289}{1000000}$ = 0.000289

(vii) Ninety five-hundredths = $\dfrac{95}{100}$ = 0.95

Convert into a decimal fraction:

(i) $\dfrac{3}{4}$

(ii) $\dfrac{3}{40}$

(iii) $\dfrac{1}{125}$

(iv) $\dfrac{7}{25}$

Answer

To convert into a decimal fraction, we multiply the numerator and the denominator by a number so that the denominator becomes 10 or a higher power of 10.

(i) $\dfrac{3}{4} = \dfrac{3 \times 25}{4 \times 25} = \dfrac{75}{100}$ = 0.75

(ii) $\dfrac{3}{40} = \dfrac{3 \times 25}{40 \times 25} = \dfrac{75}{1000}$ = 0.075

(iii) $\dfrac{1}{125} = \dfrac{1 \times 8}{125 \times 8} = \dfrac{8}{1000}$ = 0.008

(iv) $\dfrac{7}{25} = \dfrac{7 \times 4}{25 \times 4} = \dfrac{28}{100}$ = 0.28

Change the given decimal fraction to fraction in its lowest terms:

0.05

Answer

To change the given decimal fractions, remove the decimal point and write in the denominator as many zeroes to the right of 1 as there are digits in the decimal part.

0.05 = $\dfrac{5}{100}$ = $\dfrac{1}{20}$

Change the given decimal fraction to fraction in its lowest terms:

3.95

Answer

To change the given decimal fractions, remove the decimal point and write in the denominator as many zeroes to the right of 1 as there are digits in the decimal part.

3.95 = $\dfrac{395}{100}$ = $\dfrac{79}{20} = 3\dfrac{19}{20}$

Change the given decimal fraction to fraction in its lowest terms:

4.005

Answer

To change the given decimal fractions, remove the decimal point and write in the denominator as many zeroes to the right of 1 as there are digits in the decimal part.

4.005 = $\dfrac{4005}{1000}$ = $\dfrac{801}{200} = 4\dfrac{1}{200}$

Change the given decimal fraction to fraction in its lowest terms:

0.876

Answer

To change the given decimal fractions, remove the decimal point and write in the denominator as many zeroes to the right of 1 as there are digits in the decimal part.

0.876 = $\dfrac{876}{1000}$ = $\dfrac{219}{250}$

Change the given decimal fraction to fraction in its lowest terms:

50.06

Answer

To change the given decimal fractions, remove the decimal point and write in the denominator as many zeroes to the right of 1 as there are digits in the decimal part.

50.06 = $\dfrac{5006}{100}$ = $\dfrac{2503}{50} = 50\dfrac{3}{50}$

Change the given decimal fraction to fraction in its lowest terms:

0.01075

Answer

To change the given decimal fractions, remove the decimal point and write in the denominator as many zeroes to the right of 1 as there are digits in the decimal part.

0.01075 = $\dfrac{1075}{100000}$ = $\dfrac{43}{4000}$

Change the given decimal fraction to fraction in its lowest terms:

4.8806

Answer

To change the given decimal fractions, remove the decimal point and write in the denominator as many zeroes to the right of 1 as there are digits in the decimal part.

4.8806 = $\dfrac{48806}{10000}$ = $\dfrac{24403}{5000} = 4\dfrac{4403}{5000}$