Question

What is 0.365 as a fraction?

Answer 1

`0.365=73/200`

Explanation:

A number `abcd.lmnpq...` can be expanded as

`axx10^3+bxx10^2+cxx10^1+d+l/10+m/10^2+n/10^3+p/10^4+q/10^5+.......`

Hence `0.365` is

`3/10+6/10^2+5/10^3`

= `3/10+6/100+5/1000`

= `(3xx100)/(10xx100)+(6xx10)/(100xx10)+5/1000`

= `300/1000+60/1000+5/1000`

= `365/1000`

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

`(73xx5)/(200xx5)=(73xxcancel5)/(200xxcancel5)=73/200`

Answer 2

`73/200`

Explanation:

put `" "0.365" "`over `1`

`0.365/1`

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

`0.365/1 xx1000/1000=365/1000`

now cancel down

divide by `5`

`365/100=73/200`

Answer 3

`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 = 365/1000`

`(365 div 5)/(1000 div 5) = 73/200" "larr` simplify