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

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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 divide the numerator and denominator of the fraction with the highest common factor of 275 and 1000 which is 25

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

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 divide the numerator and denominator of the fraction with the highest common factor of 564 and 1000 which is 4

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

Step 4:

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