Question

What is 69 divided by 26?

Answer 1

`69/26=2.6538....`

Explanation:

`color(white)(xxxxxxx)2 .color(white)(x)6 color(white)(x)5color(white)(x)3color(white)(x)8`
`color(white)(xx) 26| bar(6color(white)(x)9color(white)(x).0color(white)(x) 0)color(white)(x) 0`
`color(white)(xxxxx)ul(5color(white)("x)2)color(red)(darr`
`color(white)(xxxxx)1color(white)(x)7 color(white)(x) "0"`
`color(white)(xxxxx)ul(1color(white)(x)5color(white)(x)6)`
`color(white)(xxxxxxx)1color(white)(x)4color(white)(x) "0"`
`color(white)(xxxxxxx)ul(1color(white)(x)3color(white)(x)0`
`color(white)(xxxxxxxxx) 1color(white)(x)0 color(white)(x) "0"`
`color(white)(xxxxx'xxxxx)ul(7 color(white)(x) 8 )"`
`color(white)(xxxxxxxxxxx)2color(white)(x)2color(white)(x)0`
`color(white)(xxxxxxxxxxx) ul(2color(white)(x)0 color(white)(x)8)`
`color(white)(xxxxxxxxxxxxx)1color(white)(x)2`

and hence

`69/26=2.6538....`

Note: As denominator is `26=2xx13`, leaving `2` as it is a factor of `10`, the digits should repeat from `13^(th)` digit i.e. after `12` digits.

Answer 2

`69/26 = 2 17/26`

Explanation:

Shwetank Mauria has shown the long division method very clearly.

The answer will be a pretty uncomfortable recurring decimal.

Another option is to use fractions and change an improper fraction to a mixed number. The resulting fraction is also pretty awkward, but is has the advantage of being exact, whereas a decimal answer, by necessity, has to be rounded off.

`69 div 26 = 69/26`

`69/26 = 2 17/26`

Recall the method:

`2xx26 = 52" "larr` whole number is 2

`69-52 = 17" "larr` this gives the remainder.

The remainder is a fraction of `26`

Hence `2 17/26`