Fractions, decimals, and percents are three ways to describe the same quantity. Learning to convert among them helps you compare numbers, solve proportions, read data displays, and understand real-world rates like discounts, grades, and interest. A single value can look very different in each form, so conversion skills help you see when quantities are equal.
These conversions are a core tool for algebra, science, finance, and everyday decision making.
To convert a fraction to a decimal, divide the numerator by the denominator. To convert a decimal to a percent, multiply by 100 and add the percent sign, while converting a percent to a decimal means dividing by 100. Some fractions make terminating decimals, like 1/4 = 0.25, while others make repeating decimals, like 1/3 = 0.333...
Percent means out of 100, so many conversions become easier when you rewrite a value with denominator 100.
Key Facts
- Fraction to decimal: divide the numerator by the denominator, so a/b = a ÷ b.
- Decimal to percent: multiply by 100, so 0.72 = 72%.
- Percent to decimal: divide by 100, so 35% = 0.35.
- Percent to fraction: write over 100 and simplify, so 45% = 45/100 = 9/20.
- Decimal to fraction: use place value, so 0.375 = 375/1000 = 3/8.
- A fraction has a terminating decimal if its simplified denominator has only factors of 2 and/or 5.
Vocabulary
- Fraction
- A number written as a ratio of two whole numbers, with a numerator over a denominator.
- Decimal
- A number written using place value and a decimal point to show parts of a whole.
- Percent
- A number expressed as parts per 100, shown with the percent symbol.
- Terminating decimal
- A decimal that ends after a finite number of digits.
- Repeating decimal
- A decimal in which one digit or group of digits repeats forever.
Common Mistakes to Avoid
- Moving the decimal the wrong direction when converting between decimals and percents is wrong because multiplying by 100 moves the decimal two places right, while dividing by 100 moves it two places left.
- Forgetting to simplify a fraction after converting from a percent is wrong because values like 40/100 and 2/5 are equal, but simplified form is usually expected.
- Treating every decimal as terminating is wrong because fractions such as 1/3 and 2/11 produce repeating decimals that continue forever.
- Dividing the denominator by the numerator when converting a fraction to a decimal is wrong because a/b means numerator divided by denominator, not denominator divided by numerator.
Practice Questions
- 1 Convert 7/8 to a decimal and a percent.
- 2 Convert 0.06 to a fraction in simplest form and to a percent.
- 3 Explain why 3/5, 0.6, and 60% all represent the same amount.