Question

How do you write 709.40625 as a mixed number?

Answer 1

See a solution process below:

Explanation:

First, we can rewrite this number as:

`709 + 0.40625`

Next we can write the decimal portion as:

`709 + 40625/100000`

Then we can reduce the fraction as:

#709 + 40625/100000 => 709 + (3125 xx 13)/(3125 xx 32) =>#

`709 + (color(red)(cancel(color(black)(3125))) xx 13)/(color(red)(cancel(color(black)(3125))) xx 32) => 709 + 13/32 =>`

`709 13/32`

Answer 2

`709.40625 = 709 13/32`

Explanation:

This is a terminating decimal, so we know that the denominator of the fraction will be a power of `10`

`709.40625" "larr` denominator wil be `10^5`

Write it as a whole number and a fraction:

`709 40625/100000" "larr` now simplify.

`5 and 25` are obviously factors of top and bottom, but if you are familiar with the decimal forms of the eighths, you will know that `125` is also a factor.

`(40625div125)/(100000div125) = 325/800`

`(325div25)/(800div25) =13/32" "larr` simplest form.