What is 0.365 as a fraction?

Apr 17, 2018

$0.365 = \frac{73}{200}$

Explanation:

A number $a b c d . l m n p q \ldots$ can be expanded as

$a \times {10}^{3} + b \times {10}^{2} + c \times {10}^{1} + d + \frac{l}{10} + \frac{m}{10} ^ 2 + \frac{n}{10} ^ 3 + \frac{p}{10} ^ 4 + \frac{q}{10} ^ 5 + \ldots \ldots .$

Hence $0.365$ is

$\frac{3}{10} + \frac{6}{10} ^ 2 + \frac{5}{10} ^ 3$

= $\frac{3}{10} + \frac{6}{100} + \frac{5}{1000}$

= $\frac{3 \times 100}{10 \times 100} + \frac{6 \times 10}{100 \times 10} + \frac{5}{1000}$

= $\frac{300}{1000} + \frac{60}{1000} + \frac{5}{1000}$

= $\frac{365}{1000}$

As numerator and denominator both are divisible by $5$, this reduces to

$\frac{73 \times 5}{200 \times 5} = \frac{73 \times \cancel{5}}{200 \times \cancel{5}} = \frac{73}{200}$

May 8, 2018

$\frac{73}{200}$

Explanation:

put $\text{ "0.365" }$over $1$

$\frac{0.365}{1}$

multiply top and bottom by the smallest multiple of $10$ that makes the top number a whole number

$\frac{0.365}{1} \times \frac{1000}{1000} = \frac{365}{1000}$

now cancel down

divide by $5$

$\frac{365}{100} = \frac{73}{200}$

May 13, 2018

$\frac{73}{200}$

Explanation:

By definition decimals are a way of writing fractions which have powers of $10$ as the denominator.

One decimal place represents tenths.
Two decimal places represent hundredths.
Three decimal places represent thousandths.

$0.365 = \frac{365}{1000}$

$\frac{365 \div 5}{1000 \div 5} = \frac{73}{200} \text{ } \leftarrow$ simplify