# How to Find a Decimal Equivalent to a Fraction

By Maya Austen
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A fraction is a ratio of two numbers that illustrate a part of a whole. The top, or first, number is called the numerator. It represents the part. The bottom, or last, number is called the denominator. It represents the whole. A decimal is essentially a fraction with a base 10 denominator. Every fraction can be converted into a decimal and vice versa. The process of finding the decimal equivalent of a fraction is a matter of division. If you can learn to look at a fraction as if it were a division equation, converting a fraction to a decimal is simple.

## Convert Fraction to Decimal

### Step 1

Write down the fraction. For example, consider 2/5.

### Step 2

Rewrite the fraction as a division problem.

For example: 2 / 5 =

Written as a division problem, the fraction’s numerator functions as the dividend. The fraction’s denominator functions as the divisor. The dividend is the number being divided. The divisor is the number that the dividend is being divided by. In this example, 2 is the dividend and 5 is the divisor. Therefore, 2 is divided by 5.

### Step 3

Solve the equation. The result is the decimal equivalent of the fraction.

For example: 2 / 5 = 0.4

## Convert Decimal to Fraction

### Step 1

Write down the decimal number.

For example: 0.4

### Step 2

Determine the place value of the last number in the decimal. For instance, decide if the number in the last place of the decimal in the tenths, hundredths or thousandths place. The tenths place is the first place to the right of the decimal point. Then comes the hundredths place and then the thousandths. In the example, 0.4, the last number in the fraction (4) is in the tenths place.

### Step 3

Rewrite the decimal as a fraction with the number in the decimal acting as the numerator. Take the “ths” off of the number placement determined in Step 2, the result is the fraction’s denominator.

For example: 4/10.

### Step 4

Simplify the fraction. Divide the numerator and denominator by the common multiple, 2. The result in the example is 2/5.