Question

Using long division, write the rational number 7/16 as a terminating decimal?

Answer 1

`7/16=0.4375`

Explanation:

Let us first write `7` as `7.000000000.....` and
divide by `16`.

As `7` units are equal to `70` one-tenths, `16` goes `4` times and `6` one-tenths are left. These are equal to `60` one-hundredths and it goes `3` times and `12` one-hundredths are left. This way, we can go on, till we get zero and we get terminating decimal or numbers start repeating and we get repeating numbers.

`ul16|7.0000000|ul(0.4375)`
`color(white)(xx)ul(64)`
`color(white)(xxx)60`
`color(white)(xxx)ul(48)`
`color(white)(xxx)120`
`color(white)(xxx)ul(112)`
`color(white)(xxxX)80`
`color(white)(xxxx)ul(80)`
`color(white)(xxxx)X`

Hence `7/16=0.4375`