A terminating decimal can be written as an integer over a power of ten, then simplified using the greatest common factor.
Write the place value
For 0.75, write 75/100 because there are two digits after the decimal. The denominator is 100, not 10.
Simplify the fraction
The GCF of 75 and 100 is 25. Divide both by 25 to get 3/4. Multiplying or dividing only the numerator would change the value.
Negative and mixed values
Keep the negative sign on the numerator or in front of the fraction. For 2.25, split the whole part and decimal part to get 2 + 1/4 = 2 1/4.
Repeating decimals
A repeating decimal needs a different algebraic method or a stated approximation. Do not present a rounded repeating decimal as an exact terminating fraction without labeling the approximation.
Sources
The figures and rules in this guide are checked against:
- Fraction — Wolfram MathWorld
- Repeating Decimal — Wolfram MathWorld
- Greatest Common Divisor — Wolfram MathWorld
- Converting decimals to fractions — Khan Academy