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

Rules to convert a decimal to a proper fraction in simplest form.(Advanced)

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 0.275 to a proper fraction in simplest form.

Solution

Step 1:

We drop the decimal and write the number 275 as the numerator of a fraction.

Step 2:

The place value of the last digit 5 is a thousandth. So, we write 1000 as the denominator of the fraction to get

$0.275 = frac{275}{1000}$

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 275 and 1000 which is 25

$frac{(275 span 25)}{(1000 span 25)} = frac{11}{40}$

Step 4:

So, $0.275 = frac{11}{40}$ as a proper fraction in simplest form.

Convert decimal 0.564 to a proper fraction in simplest form.

Solution

Step 1:

We drop the decimal and write the number 564 as the numerator of a fraction.

Step 2:

The place value of the last digit 4 is a thousandth. So, we write 1000 as the denominator of the fraction to get

$0.564 = frac{564}{1000}$

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 564 and 1000 which is 4

$frac{(564 span 4)}{(1000 span 4)} = frac{141}{250}$

Step 4:

So, $0.564 = frac{141}{250}$ as a proper fraction in simplest form.