How do you round 315.757 to the nearest hundredth?

##315.76##

The cut of place for ##1/100ths## is the second decimal place. So the numbers we are interested in are the red ones below.

##color(red)(315.75)7##

But the 7 after the 5 is such that ##7>=5## so we round up giving

##315.76## '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Another example

Suppose we had: ##color(red)(23.58)3##

The 3 is such that ##3<5## so we round down (do not change anything giving 23.58 '................................................................ Suppose we had: ##color(red)(23.58)6##

##6>=5## so we round up giving 23.59