Question

Write the below decimals as fractions in lowest terms.
A) 0.60
B) 0.05
C) 0.75
D) 0.18
E) 0.2
F) 0.066

Answer 1

Hint: To convert a decimal value to a fraction we need to observe the number of digits after the decimal point.

Complete step-by-step answer:
We have to multiply and divide the decimal value with a number which will be in the form of ${10^n}$, n value equals the number of digits after the decimal point. Then we simplify the fraction.

A) 0.60, here after decimal point we have 2 digits, So multiplying and dividing it with ${10^2}$
 $ \Rightarrow \dfrac{{0.60 \times 100}}{{100}} = \dfrac{{60}}{{100}} = \dfrac{3}{5}$

B) 0.05, here after decimal point we have 2 digits, So multiplying and dividing it with ${10^2}$ $ \Rightarrow \dfrac{{0.05 \times 100}}{{100}} = \dfrac{5}{{100}} = \dfrac{1}{{20}}$

C) 0.75, here after decimal point we have 2 digits, So multiplying and dividing it with ${10^2} = 100$$ \Rightarrow \dfrac{{0.75 \times 100}}{{100}} = \dfrac{{75}}{{100}} = \dfrac{3}{4}$

D) 0.18, here after decimal point we have 2 digits, So multiplying and dividing it with ${10^2} = 100$ $ \Rightarrow \dfrac{{0.18 \times 100}}{{100}} = \dfrac{{18}}{{100}} = \dfrac{9}{{50}}$

E) 0.2, here after decimal point we have 2 digits, So multiplying and dividing it with ${10^1} = 10$
 $ \Rightarrow \dfrac{{0.2 \times 10}}{{10}} = \dfrac{2}{{10}} = \dfrac{1}{5}$

F) 0.066, here after decimal point we have 2 digits, So multiplying and dividing it with ${10^3} = 1000$$ \Rightarrow \dfrac{{0.066 \times 1000}}{{1000}} = \dfrac{{66}}{{1000}} = \dfrac{{33}}{{500}}$

Note: Three steps we need to keep in mind while converting decimal numbers to fractions is:
I. Observe the number of digits after the decimal point.
II. Find a multiplication factor to multiply both denominator and numerator, to get a fraction.
III. Reduce the resulting fraction to its simplest form.