Converting Between Fractions and Decimals: Practice

One digit follows the point, so the denominator is ten.

$0.9 = \frac{9}{10}$

Two digits follow the point, so the denominator is a hundred and the two digits sit on top.

$0.21 = \frac{21}{100}$

The fraction bar means divide the numerator by the denominator, top by bottom.

$\frac{3}{4} = 3 \div 4$

So $\tfrac{3}{4}$ is $3$ divided by $4$, not $4$ divided by $3$.

A fraction is a division, so compute $1 \div 4$.

$\frac{1}{4} = 1 \div 4 = 0.25$

This is a quarter, the same as $25$ cents in a dollar.

Three tenths means the digit $3$ sits in the first place after the point.

$\frac{3}{10} = 0.3$

Nine tenths means the digit $9$ sits in the tenths place, the first place after the point.

$\frac{9}{10} = 0.9$

One digit follows the point, so $0.5 = \tfrac{5}{10}$. Reduce by dividing the top and bottom by $5$.

$\frac{5}{10} = \frac{5 \div 5}{10 \div 5} = \frac{1}{2}$

The form $\tfrac{5}{10}$ is equal but not in lowest terms.

Three hundredths means the $3$ lands in the second place after the point, so a $0$ holds the tenths place.

$\frac{3}{100} = 0.03$

Scale to a denominator of ten, since $5 \times 2 = 10$, by multiplying the top and bottom by $2$.

$\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10} = 0.4$

One digit follows the point, so the denominator is ten.

$0.3 = \frac{3}{10}$

It is already in lowest terms, since $3$ and $10$ share no common factor larger than $1$.

Seven tenths puts the $7$ in the tenths place, the first place after the point.

$\frac{7}{10} = 0.7$

Two digits follow the point, so the denominator is a hundred and the two digits sit on top.

$0.11 = \frac{11}{100}$

Since $11$ is prime and does not divide $100$, this is already in lowest terms.