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 spanide the numerator and denominator of the fraction with the highest common factor of 45 and 100 which is 5

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

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 spanide the numerator and denominator of the fraction with the highest common factor of 74 and 100 which is 2

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

Step 4:

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