How to Convert Decimal to Fraction

Quick Scoop

To convert a decimal to a fraction, you turn the decimal into “something over a power of 10” and then simplify that fraction.

Step‑by‑Step: Simple (Non‑repeating) Decimals

Let’s build a clear recipe you can reuse.

Core method

  1. Write the decimal over 1
    Example: $$0.75 = \dfrac{0.75}{1}$$.[7][1]
  2. Multiply to remove the decimal point
    Count how many digits are after the decimal:
    • 1 digit → multiply top and bottom by 10
    • 2 digits → multiply by 100
    • 3 digits → multiply by 1000, and so on
      • [3][1][7]
    For $$0.75$$, there are 2 digits after the decimal, so multiply by 100: $$ \dfrac{0.75}{1} \times \dfrac{100}{100} = \dfrac{75}{100} $$
  3. Simplify the fraction Divide numerator and denominator by their greatest common factor (GCF).[5][9][1] For $$\dfrac{75}{100}$$, divide by 25: $$ \dfrac{75}{100} = \dfrac{3}{4} $$
So 0.75=340.75=\dfrac{3}{4}0.75=43​.

Quick Examples

Example 1: 0.4

  • Write it over 1: $$\dfrac{0.4}{1}$$
  • 1 digit after the decimal → multiply by 10: $$\dfrac{0.4}{1} \times \dfrac{10}{10} = \dfrac{4}{10}$$[5][7]
  • Simplify: divide top and bottom by 2 → $$\dfrac{2}{5}$$
    • [5]
Result: 0.4=250.4=\dfrac{2}{5}0.4=52​.

Example 2: 0.625

  • $$\dfrac{0.625}{1}$$
  • 3 digits after decimal → multiply by 1000: $$\dfrac{0.625}{1} \times \dfrac{1000}{1000} = \dfrac{625}{1000}$$[1][3]
  • Simplify: divide by 125 → $$\dfrac{5}{8}$$.
    • [9][1]
Result: 0.625=580.625=\dfrac{5}{8}0.625=85​.

Example 3: 2.35 (decimal bigger than 1)

You can think of this two ways, both valid.

Method A: Treat the whole thing at once

  • $$\dfrac{2.35}{1}$$
  • 2 digits after decimal → multiply by 100 → $$\dfrac{235}{100}$$
  • Simplify: divide by 5 → $$\dfrac{47}{20}$$
4720\dfrac{47}{20}2047​ is an improper fraction; as a mixed number it’s 27202\dfrac{7}{20}2207​.

Method B: Separate integer and decimal part

  • Write $$2.35 = 2 + 0.35$$
  • Convert $$0.35$$: $$\dfrac{35}{100} = \dfrac{7}{20}$$
  • Combine: $$2 + \dfrac{7}{20} = 2 \dfrac{7}{20}$$
Same final answer, different viewpoint.

Table: Common Decimals to Fractions

[5] [5] [9][1] [5] [5] [1][9] [3][9]
Decimal As a starting fraction Simplified fraction
0.1 1/10 1/10
0.2 2/10 1/5
0.25 25/100 1/4
0.4 4/10 2/5
0.5 5/10 1/2
0.75 75/100 3/4
0.125 125/1000 1/8

Repeating Decimals (Bonus View)

Repeating decimals (like 0.3‾0.\overline{3}0.3, 0.36‾0.\overline{36}0.36) need one extra algebra trick.

Example: $$0.\overline{3}$$

  1. Let $$x = 0.\overline{3}$$.
    2. [7]
  2. Multiply by 10 (one repeating digit): $$10x = 3.\overline{3}$$.
  3. Subtract: $$10x - x = 3.\overline{3} - 0.\overline{3} = 3$$.
  4. So $$9x = 3 \Rightarrow x = \dfrac{1}{3}$$.
    5. [7][9]
So 0.3‾=130.\overline{3}=\dfrac{1}{3}0.3=31​.

Mini Forum‑Style Take

“Whenever I forget how to convert a decimal to a fraction, I just remember: put it over 1, kill the decimal with a power of 10, then reduce. Works for almost everything I see in homework.”

This little three‑step mantra is what most online calculators and tutorials are doing under the hood when they show “steps” for decimal‑to‑fraction conversion.

SEO Bits (for your post)

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TL;DR:
Write the decimal over 1, multiply top and bottom by 10, 100, 1000, etc. until the decimal disappears, then simplify the fraction by dividing by the GCF.

Information gathered from public forums or data available on the internet and portrayed here.