Question

Express each decimal in expanded form and as a fraction.

a. 4.6    b. 0.75    c. 1.234    d. 4.06

Answer 1

We need to express each of the following decimals in expanded form and as a fraction.

(a)

We have \(4.6\), in expanded form \(4.6\) can be expressed as-

$$ 4.6=4+\frac{6}{10} $$

In fraction \(4.6\) can be expressed as-

$$ \begin{aligned} 4.6 &=\frac{4.6 \times 10}{10} \\ &=\frac{46 \times \frac{1}{2}}{10 \times \frac{1}{2}} \\ &=\frac{23}{5} \end{aligned} $$

(b)

We have \(0.75\), in expanded form \(0.75\) can be expressed as-

$$ 0.75=\frac{7}{10}+\frac{5}{100} $$

In fraction \(0.75\) can be expressed as-

$$ \begin{aligned} 0.75 &=\frac{0.75 \times 100}{100} \\ &=\frac{75 \times \frac{1}{25}}{100 \times \frac{1}{25}} \\ &=\frac{3}{4} \end{aligned} $$

(c)

We have \(1.234\), in expanded form \(1.234\) can be expressed as-

$$ 1.234=1+\frac{2}{10}+\frac{3}{100}+\frac{4}{1000} $$

In fraction \(1.234\) can be expressed as-

$$ \begin{aligned} 1.234 &=\frac{1.234 \times 1000}{1000} \\ &=\frac{1234 \times \frac{1}{2}}{1000 \times \frac{1}{2}} \\ &=\frac{617}{500} \end{aligned} $$

(c)

We have \(4.06\) in expanded form \(4.06\) can be expressed as-

$$ 4.06=4+\frac{6}{100} $$

In fraction \(4.06\) can be expressed as-

$$ \begin{aligned} 4.06 &=\frac{4.06 \times 100}{100} \\ &=\frac{406 \times \frac{1}{2}}{100 \times \frac{1}{2}} \\ &=\frac{203}{50} \end{aligned} $$