Connecting Fractions & Decimals

≈ 20 min

Fractions and decimals are two ways of writing the same parts of a whole. The link runs through tenths and hundredths:

\frac{7}{10} = 0.7, \qquad \frac{45}{100} = 0.45.

A few worth knowing by heart: $\frac{1}{2} = 0.5$ , $\frac{1}{4} = 0.25$ , $\frac{3}{4} = 0.75$ , $\frac{1}{10} = 0.1$ .

Worked example. Write $0.6$ as a fraction in simplest form. Read it as $6$ tenths: $0.6 = \frac{6}{10}$ , and simplifying gives $\frac{6}{10} = \frac{3}{5}$ .

Which decimal is equal to $\dfrac{1}{2}$ ?

$0.2$

$0.5$

$0.12$

$0.25$

Write $\dfrac{7}{10}$ as a decimal.

Write $0.25$ as a common fraction in simplest form, as a fraction like a/b.

Which list is ordered from smallest to largest?

$0.5,\ \tfrac{1}{4},\ 0.75$

$\tfrac{1}{4},\ 0.5,\ 0.75$

$0.75,\ 0.5,\ \tfrac{1}{4}$

$\tfrac{1}{4},\ 0.75,\ 0.5$