How do you Convert a number to a Fraction

The short answer: To convert a number to a fraction, write it with an integer numerator and a power-of-10 denominator (for terminating decimals or percentages) or use the algebra method for repeating decimals, then simplify by dividing numerator and denominator by their greatest common divisor.

Explanation

1) Terminating decimals (e.g., 0.75, 2.5)

Steps:

  1. Count decimal places. Multiply numerator and denominator by a power of 10 to remove the decimal.
  2. Simplify the resulting fraction.

Examples:

  • $0.75 = \dfrac{75}{100} = \dfrac{3}{4}$ (divide top and bottom by 25).
  • $2.5 = \dfrac{25}{10} = \dfrac{5}{2}$ (or $2\frac{1}{2} = \dfrac{5}{2}$).

2) Repeating decimals (e.g., $0.\overline{3}$, $0.1\overline{6}$)

Use algebra:

  • Let $x = 0.\overline{3}$. Then $10x = 3.\overline{3}$. Subtract: $9x = 3$, so $x = \dfrac{1}{3}$.
  • For non‑repeating + repeating part (example $x=0.1\overline{6}$): nonrepeating length $m=1$, repeating length $n=1$.
  • Compute $10^{m+n}x – 10^m x = $ integer difference.
  • $100x = 16.\overline{6}$ and $10x = 1.\overline{6}$ so $90x = 15$, hence $x = \dfrac{15}{90} = \dfrac{1}{6}$.

General formula: if decimal has nonrepeating part a and repeating part b,
$$x = \frac{\text{(all digits up to end of first repeat)} – \text{(nonrepeating digits)}}{10^{m+n} – 10^m}.$$

3) Percentages

Replace % with division by 100, then simplify:

  • $45\% = \dfrac{45}{100} = \dfrac{9}{20}$.

4) Mixed numbers

Convert the fractional part and add to the integer, or convert whole number to fraction over 1:

  • $2.75 = \dfrac{275}{100} = \dfrac{11}{4}$.

5) Simplify by GCD

Always divide numerator and denominator by their greatest common divisor (GCD) to get the fraction in lowest terms.

Quick checklist

  • Terminating decimal: multiply by $10^{\text{decimal places}}$, simplify.
  • Repeating decimal: use algebraic subtraction (multiply by $10^{m+n}$ and $10^m$, subtract), simplify.
  • Percent: put over 100, simplify.
  • Mixed: convert to improper fraction or separately convert integer + fraction.

If you want, give me a specific number (like 0.142857, 3.125, or 12.5%) and I’ll convert it step-by-step.

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