# 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 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.