Converting a decimal to a proper fraction in simplest form: Basic

We find it useful sometimes to convert a decimal to a fraction form and reduce it to simplest terms.

Rules to convert a decimal to a proper fraction in simplest form.

• We drop the decimal point and write the number as the numerator of a fraction.

• We take the place value of the last digit of the decimal number and write it as the denominator of the fraction.

• Then we reduce the fraction to the simplest form.

Convert decimal 0.45 to a proper fraction in simplest form

Solution

Step 1:

We drop the decimal and write the number 45 as the numerator of a fraction.

Step 2:

The place value of the last digit 5 is a hundredth. So, we write 100 as the denominator of the fraction to get

$0.45 = \frac{45}{100}$

Step 3:

To reduce the fraction to the simplest form, we divide the numerator and denominator of the fraction with the highest common factor of 45 and 100 which is 5

$0.336 = \frac{(45 \div 5)}{(100 \div 5)} = \frac{9}{20}$

Step 4:

So, $0.45 = \frac{9}{20}$ as a proper fraction in simplest form.

Convert decimal 0.74 to a proper fraction in simplest form.

Solution

Step 1:

We drop the decimal and write the number 74 as the numerator of a fraction.

Step 2:

The place value of the last digit 4 is a hundredth. So we write 100 as the denominator of the fraction to get

$0.74 = \frac{74}{100}$

Step 3:

To reduce the fraction to the simplest form, we divide the numerator and denominator of the fraction with the highest common factor of 74 and 100 which is 2

$\frac{(74 \div 2)}{(100 \div 2)} = \frac{37}{50}$

Step 4:

So, $0.74 = \frac{37}{50}$ as a proper fraction in simplest form.