This worksheet is about lower and upper bounds.
Suppose we've rounded a number to the nearest whole number and get 14.
Numbers that round up to 14 include 13.9, 13.75, 13.694, 13.5. The smallest of these is 13.5. This is called the LOWER BOUND.
Anything smaller will round down to 13.
Larger numbers that round down to 14 include 14.1, 14.34968, 14.49. The largest of these is 14.4999999... This is the UPPER BOUND, which we write as 14.5.
We write these bounds as an inequality.
13.5 ≤ n < 14.5
Note: The lower bound is included in the inequality, but the upper bound is not – it would round up.
Find the upper and lower bounds for 8500 which has been rounded to the nearest hundred.
8499, 8470, 8450 would round up.
8450 is the smallest, so this is the LOWER BOUND.
8501, 8548, 8549 would round down.
8549.999999 is the largest, so we say that 8550 is the UPPER BOUND.
8450 ≤ n < 8550