Math 208, Section 2.5 Solutions: Rounding Decimal Numbers
1. Round 2.1349 to the nearest hundredth. Explain in words why you round the
decimal number the way you do. Use a number line to support your explanation.
The solution is 2.13. Nearest hundredth means that we want to find the closest number
out of the list
..., 2.09, 2.10, 2.11, 2.12, 2.13, 2.14, 2.15, ...
2.1349 is in between 2.13 and 2.14 and it is just a little closer to 2.13.
2. Round 27,003 to the nearest hundred. Explain in words why you round the
decimal number the way you do. Use a number line to support your explanation.
The solution is 27,000. Nearest hundred means we want to find the closest number out
of the list
..., 26,800; 26,900; 27,000; 27,100; 27,200; ...
27,0003 is obviously closest to 27,000. It is also true that if we round 27003 to the
nearest thousand, we get the same number 27000.
4. Adam has made up his own method of rounding. Starting at the rightmost place
in a decimal number, he keeps rounding to the value of the next place to the left
until he reaches the place to which the decimal number was to be rounded. For
example, Adam would use the following steps to round 11.3524 to the nearest tenth:
11.3524 11.352 11.35 11.4
Is Adam’s method a valid way to round? Explain why or why not.
Adam’s method will often work. It may fail if there are some 5’s involved, though. For
instance, to round 14.49 to the nearest whole number we would get
13.49 → 13.5 → 14
where we have used the convention that “5’s round up.” Even 13.45 will mess Adam up,
since he will first round to 13.5 and then to 14.
If you use the “5’s round down” convention, then 13.49 will round correctly using
Adam’s method but 13.51 will not. If you use the convention that “5’s round to the
nearest even number” then Adam will be wrong on 13.49 again.
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