how do you turn a fraction into a decimal

To turn a fraction into a decimal, you divide the top number by the bottom number: numerator ÷ denominator.

The core idea (super short)

• Take a fraction like 34\frac{3}{4}43​.
• Do the division: 3÷4=0.753÷4=0.753÷4=0.75.
• That answer (0.75) is the decimal form of the fraction.

Step‑by‑step method (long division)

Use this when the numbers don’t divide evenly in your head.

1. Write the fraction as a division:
   • ab\frac{a}{b}ba​ means a÷ba÷ba÷b.
   • Example: 18=1÷8\frac{1}{8}=1÷881​=1÷8.
2. If the top number (numerator) is smaller than the bottom number (denominator), add a decimal and a zero:
   • 1 ÷ 8 becomes 1.0 ÷ 8.
   • You now divide 10 by 8 (because of the 0 after the decimal).
3. Do long division:
   • 8 goes into 10 one time → write 0.1 so far.
   • Remainder is 2 (because 10 − 8 = 2).
   • Bring down another 0 → now you divide 20 by 8.
   • 8 goes into 20 two times → write 0.12.
   • Remainder is 4 (20 − 16 = 4).
   • Bring down another 0 → divide 40 by 8.
   • 8 goes into 40 five times → write 0.125.
   • Remainder is 0, so you’re done: 18=0.125\frac{1}{8}=0.12581​=0.125.

You can stop when:

• The remainder becomes 0 (it terminates), or
• You see a pattern repeating (like 0.3333…) and write it as a repeating decimal (often with a bar on top in school).

Shortcut when the denominator is 10, 100, 1000…

If the bottom of the fraction is a power of 10 (10, 100, 1000, …), you don’t need long division.

• 710=0.7\frac{7}{10}=0.7107​=0.7 (one zero → one digit after the decimal).
• 34100=0.34\frac{34}{100}=0.3410034​=0.34 (two zeros → two digits after the decimal).
• 8751000=0.875\frac{875}{1000}=0.8751000875​=0.875 (three zeros → three digits after the decimal).

So: count the zeros in the denominator; that’s how many digits go after the decimal.

Trick to make the denominator a power of 10

Sometimes you can turn a “nice” fraction into tenths, hundredths, or thousandths. Example: 78\frac{7}{8}87​

1. Ask: what can I multiply 8 by to get 100 or 1000?
   • 8 × 125 = 1000.
2. Multiply top and bottom by the same number:
   • 78=7×1258×125=8751000\frac{7}{8}=\frac{7×125}{8×125}=\frac{875}{1000}87​=8×1257×125​=1000875​.
3. Now use the power‑of‑10 trick:
   • 8751000=0.875\frac{875}{1000}=0.8751000875​=0.875.

Mixed numbers (like 2 ½)

If you have a mixed fraction, convert the fraction part , then add the whole number. Example: 2142\frac{1}{4}241​

1. Convert 14\frac{1}{4}41​ to decimal:
   • 1 ÷ 4 = 0.25.
2. Add the whole number:
   • 2 + 0.25 = 2.25.

So 214=2.252\frac{1}{4}=2.25241​=2.25.

Quick mental examples

• 12=0.5\frac{1}{2}=0.521​=0.5
• 14=0.25\frac{1}{4}=0.2541​=0.25
• 34=0.75\frac{3}{4}=0.7543​=0.75
• 15=0.2\frac{1}{5}=0.251​=0.2
• 25=0.4\frac{2}{5}=0.452​=0.4
• 35=0.6\frac{3}{5}=0.653​=0.6

These are worth memorizing because they show up a lot.

TL;DR

• Write the fraction as a division: numerator ÷ denominator.
• Use long division if it doesn’t come out evenly.
• If the denominator is 10, 100, 1000, just place the decimal point according to the zeros.
• For mixed numbers, convert the fraction part and add it to the whole number.

If you tell me a specific fraction you’re stuck on, I can walk through that exact one with you.