I'm stuck with rounding decimals and have been for years 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?
 A: To round to either $8.6$ or $8.7$, compare them with the middle value of both which is $8.65$. The question is do you have :$$8.647 < 8.65\qquad \text{ or } \qquad 8.647 \ge 8.65$$
In the first case you round down to $8.6$, in the second case you round up to $8.7$.
Same goes with $8.565656$, take the middle value of $8.56$ and $8.57$, which do you have :$$8.565656 < 8.565\qquad \text{ or } \qquad 8.565656 \ge 8.565$$
If your problem is comparing decimals, I suggest you have a look at this Khan Academy video which explains it well.
A: 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: $8.6$
