TITLE: I'm stuck with rounding decimals and have been for years
QUESTION [5 upvotes]: I'm in year 10 and have a B grade - yet still manage to mess it up when I face a question regarding decimals. For example:
Round 8.647 to one decimal place.
Would this be 8.7 or 8.6 as I have never understood if the third number affects the second number first.
Also recurring decimals, say for example:
Round 8.56565656 to two decimal places
Would this be 8.67 and the first and second are rounded, or 8.57, or 8.56?
Finally,
Would 8.045 = 8.05? or 8.15?

REPLY [2 votes]: Suppose you want a number correct to $i$ decimal places. Just look at the $i+1$ th digit. If its a $5$ or greater, round up. If its a $4$ or lower, round down.

Round down = forget everything after the $i$th digit
Round up = forget everything after the $i$th digit, and increment the $i$th digit by $1$.

For example, if you want $8.647$ correct to $1$ decimal place, you need to be looking at the digit immediately after the $6$. In this case its $4$. So you round down. Final answer: $8.6$