### Conversions between Rational Numbers

Fractions to Decimals

*Method 1*

To convert a fraction to a decimal, divide the numerator by the denominator.

Example

*Procedure*: is similar to normal division except, since 8 goes into 4 zero times, a decimal point is placed after the zero and a zero added to 4 turning it into 40.

*Method 2*

Step 1: Find a number that when multiplied by the denominator, results in a product of 10, 100, 1000 or any number with a 1 followed by zeros.

Step 2: Multiply both the numerator and denominator by that number.

Step 3: Write down the new numerator, putting a decimal point one place to the right for every zero in the new denominator.

Example

Decimals to Fractions

To convert a decimal to a fraction, use the method outlined below.

Example

Fractions to Percentages

To convert a fraction to a decimal, multiply the fraction by 100.

Example

Percentages to Fractions

To convert a percentage into a fraction, follow the steps outlined below.

Step 1: Divide the percentage by 100.

Step 2: This step applies only if the percentage is not a whole number. In this case, multiply the numerator and the denominator by 10 for every digit after the decimal point (if a number has 2 digits after the decimal point, multiply by 100: 3 digits, multiply by 1000 etc).

Step 3: Reduce the fraction into its simplest form.

Examples

Decimals to Percentages

To convert a decimal into a percentage, move the decimal point two places to the right (which is the same as multiplying by 100) and add the percentage sign.

Example

Convert 0.728 into a percentage.

Percentage to Decimal

To convert a percentage into a decimal, move the decimal point two places to the left (divide by 100) and remove the percentage sign.

Example

Convert 43.2% into a decimal.