The number 89.667 rounded off to three significant figures is

89.7

Explanation:

First we have to look at the right of the digit which is going to be round. If it is 5 or greater than 5 than the number left to it should be increased by one.

For example

In given number 89.667 after three digits 8, 9, 6 the next digit is 6.

So in order to round the number to three digits 6 will rounded to 7 and value becomes 89.7

If the digit next to rounded digit is less than 5 than number will rounded as,

For example:

56.42

Rounded to three digit it will be 56.4.