Fractions, Decimals & Percents

One number, three notations — reduce and convert freely among them.

The idea

A fraction, a decimal and a percent are three ways of writing the same number, and converting among them is how we compare quantities given in different forms.

A fraction $\frac{a}{b}$ denotes the division $a \div b$. It is in lowest terms when its numerator and denominator share no common factor greater than $1$; dividing both by their greatest common factor puts it there without changing its value.

To convert a fraction to a decimal, carry out the division. To convert a decimal to a fraction, read its denominator off as a power of ten — $0.7 = \frac{7}{10}$ — and reduce.

Percent means per hundred, so $n\%$ names the fraction $\frac{n}{100}$. A percent becomes a decimal on dividing by $100$, and a decimal becomes a percent on multiplying by $100$.

To compare quantities written in different forms, convert them all to decimals and compare digit by digit, left to right.

Ways to work on it

• Walkthrough. Reduce a fraction, then convert it to a decimal and a percent.
• Practice. Convert a value into a requested form.
• Hardest. Convert to a common form and compare across all three notations.

Not sure where to start? Take the ten-question placement test.