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Q51.

Expert-verifiedFound in: Page 225

Book edition
Common Core Edition

Author(s)
Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

Pages
183 pages

ISBN
9780547587776

**Write the decimal as a fraction or mixed number.**

**$\mathbf{-}\mathbf{0}\mathbf{.}\overline{\mathbf{4}}$**

The fraction is $-\frac{4}{9}$.

Consider, the decimal $-0.\overline{4}$ provided in question

Let $x=-0\times \overline{4}$

$x=-0\xb74444.....$ …… (1)

Clearly, 4 is the only digit which is repeating in equation (1)

Multiply equation (1) by 10 on both sides,

$10x=-4\xb74444.....$ …… (2)

Subtract equation (1) from equation (2),

$\begin{array}{c}10x-x=(-4\cdot \mathrm{4444...})-(-0\cdot \mathrm{4444...})\\ 9x=-4\\ x=\frac{-4}{9}\end{array}$

Thus, the fraction number that can be formed is $\frac{-4}{9}$.

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