# What's 11.045 as a fraction?

Feb 7, 2018

$11.045 = 11 \frac{45}{1000} = 11 \frac{9}{200}$

#### Explanation:

Write the decimal fraction as a mixed number with a power of $10$ as the denominator.

$3$ decimal places indicates thousandths.

$11.045 = 11 \frac{45}{1000} \text{ } \leftarrow$ simplify

$11 \frac{45}{1000} = 11 \frac{9}{200} \text{ } \leftarrow$ divide top and bottom by $5$

Feb 7, 2018

fraction: $11.045 \times \left(\frac{1000}{1000}\right) = \frac{11045}{1000} = \frac{2209}{200}$

#### Explanation:

To make a decimal a fraction, multiply it by a power of 10 over itself ($\frac{10}{10} = 1 , \frac{100}{100} = 1$, etc) until it's a whole number. We are allowed to do this because multiplying a number by 1 doesn't change its value.

To simplify a fraction, find the Greatest Common Factor between the numerator and denominator, and divide each by this number.
Dividing the numerator and denominator by the same number is the same as dividing the overall number by 1, which doesn't change its value.

$\frac{\frac{11045}{5}}{\frac{1000}{5}} = \frac{\frac{11045}{1000}}{\frac{5}{5}} = \frac{\frac{11045}{1000}}{1}$

simplified: GCF(11045, 1000) = 5 so

$\frac{11045}{5} = 2209$

$\frac{1000}{5} = 200$

$\frac{2209}{200}$