How do you write 0.0064 as a fraction?

Oct 28, 2016

$0.0064$

$= 0 \cdot {10}^{0} + 0 \cdot {10}^{-} 1 + 0 \cdot {10}^{-} 2 + 6 \cdot {10}^{-} 3 + 4 \cdot {10}^{-} 4$

$= \frac{0}{1} + \frac{0}{10} + \frac{0}{100} + \frac{6}{1000} + \frac{4}{10000}$

$= \frac{6}{1000} + \frac{4}{10000}$

$= \frac{6 \cdot 10}{1000 \cdot 10} + \frac{4}{10000}$

$= \frac{60}{10000} + \frac{4}{10000}$

$= \frac{64}{10000}$

$= \frac{32}{5000}$

$= \frac{16}{2500}$

$= \frac{8}{1250}$

$= \frac{4}{625}$

Oct 28, 2016

$\frac{4}{625}$

Explanation:

Decimal are based on powers of 10.

The place values to the right of the decimal point are:
tenths, hundredths, thousandths, ten thousandths and so on.

$0.0064$ has 4 decimal places and therefore can be written as a fraction with a denominator as a power or 10 with 4 zeros.

$0.0064 = \frac{64}{10000}$

All that remains is to cancel it down to its simplest form.
Divide top and bottom by $16$

(64div16)/(10000 div 16

= $\frac{4}{625}$