# Convert Fractions to Decimals

### The simplest method is to use a calculator

Just divide the top of the fraction by the bottom, and read off the answer!

### Example*:* What is \frac{5}{8} as a decimal ... ?

... get your calculator and type in "5 / 8 ="

The answer should be **0.625**

### No Calculator? Use Long Division to Decimal Places

### Example: here is what long division of \frac{5}{8} looks like:

8 )5.000

0

5.0

4.8

20

16

40

40

0

In that case we inserted extra zeros and did \frac{5.000}{8} to get **0.625**

Read the Long Division to Decimal Places page for more details.

## Another Method

### Yet another method you may like is to follow these steps:

**Step 1**: Find a number you can multiply by**the bottom of the fraction**to make it 10, or 100, or 1000, or any 1 followed by 0s.**Step 2**: Multiply both top and bottom by that number.**Step 3**. Then write down just the top number, putting the decimal point in the correct spot (one space from the right hand side for every zero in the bottom number)

### Example: Convert \frac{3}{4} to a Decimal

Step 1: We can multiply 4 by 25 to become 100

Step 2: Multiply top and bottom by 25:

×25 |
||

\frac{3}{4} | = | \frac{75}{100} |

×25 |

Step 3: Write down 75 with the decimal point 2 spaces from the right (because 100 has 2 zeros);

Answer = 0.75

### Example: Convert \frac{3}{16} to a Decimal

Step 1: We have to multiply 16 by **625** to become 10,000

Step 2: Multiply top and bottom by 625:

×625 |
||

\frac{3}{16} | = | \frac{1,875}{10,000} |

×625 |

Step 3: Write down 1875 with the decimal point 4 spaces from the right (because 10,000 has 4 zeros);

Answer = 0.1875

### Example: Convert \frac{1}{3} to a Decimal

Step 1: There is no way to multiply 3 to become 10 or 100 or any "1 followed by 0s", but we can calculate an **approximate** decimal by choosing to multiply by, say, 333

Step 2: Multiply top and bottom by 333:

×333 |
||

\frac{1}{3} | = | \frac{333}{999} |

×333 |

Step 3: Now, **999 is nearly 1,000**, so let us write down 333 with the decimal point 3 spaces from the right (because 1,000 has 3 zeros):

Answer = 0.333 (accurate to only 3 decimal places!)