how do you turn a decimal into a fraction
To turn a decimal into a fraction, you follow a short set of steps: write the decimal over a power of 10, then simplify.
Basic idea (non‑repeating decimals)
Use this whenever the decimal ends , like 0.5, 2.75, 0.125.
Step‑by‑step method
- Count decimal places
- 0.5 → 1 decimal place
- 0.25 → 2 decimal places
- 3.125 → 3 decimal places
- Write it over a power of 10
- 0.5 → 510\frac{5}{10}105
- 0.25 → 25100\frac{25}{100}10025
- 3.125 → 31251000\frac{3125}{1000}10003125
- Simplify the fraction (divide top and bottom by the same number until you can’t anymore).
Quick examples
- 0.5
- One digit after the decimal → denominator 10.
- 0.5 = 510\frac{5}{10}105 → divide by 5 → 12\frac{1}{2}21.
- 0.25
- Two digits after the decimal → denominator 100.
- 0.25 = 25100\frac{25}{100}10025 → divide by 25 → 14\frac{1}{4}41.
- 2.35
- Ignore the 2 for a moment and look at 0.35.
- 0.35 = 35100\frac{35}{100}10035 → simplify to 720\frac{7}{20}207.
- Put the 2 back: 27202\frac{7}{20}2207.
Mini “recipe” you can memorize
For any terminating decimal like a.bcd:
- Drop the decimal point to get a whole number (abcd).
- Use a denominator of 10, 100, 1000, … depending on digits after the point.
- Simplify.
Example: 0.732
- 732 over 1000 → 7321000\frac{732}{1000}1000732 → divide top and bottom by 4 → 183250\frac{183}{250}250183.
What about negative decimals?
Handle the number as if it’s positive, then put the minus sign back in front.
Example: −0.4
- 0.4 → 410\frac{4}{10}104 → 25\frac{2}{5}52.
- Final answer: −25-\frac{2}{5}−52.
Tiny story to remember it
Imagine you’re zooming a picture on your phone: every decimal place is like zooming in 10× more. 0.25 is just 25 zoom‑steps out of 100, so it’s 25/100, which shrinks down to 1/4.
TL;DR:
- Count digits after the decimal.
- Put the digits as the numerator.
- Denominator = 1 with that many zeros.
- Simplify the fraction.
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