A rounded value could have been anything within half a unit either side. If x = 81 to the nearest whole number, then 80.5 ≤ x < 81.5. The lower bound is included and the upper bound is not, because 81.5 would round up to 82.
Truncating means cutting off digits without rounding. If 570 is a value truncated to 0 decimal places, then 570 ≤ m < 571. These ranges are called error intervals.
Worked example
t = 0.68, rounded to 2 decimal places. Write down the error interval.
- Half of 0.01 is 0.005.
- 0.68 − 0.005 = 0.675 and 0.68 + 0.005 = 0.685.
Answer:0.675 ≤ t < 0.685
Key words
- lower bound
- the smallest possible value
- upper bound
- the limit that the value stays below
- truncate
- cut off digits without rounding
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Common Core-referenced: HSN-Q.A.3