Foundation and Higher · error intervals
Error intervals.
Half a unit
each way.
what could it have been
before rounding?
a rounded number hides a range —
Bounds
lower bound: the smallest it could be
upper bound: where the next starts
step 1 of 4
Nearest 10
1. 80 to the nearest 10. Half of 10 is 5.
2. Go 5 below and 5 above: 75 and 85.
✓ 75 ≤ x < 85
step 2 of 4
Why ≤ and then <?
1. The lower bound itself rounds to 80.
2. The upper bound would round to 90.
✓ Always ≤ on the left, < on the right
75 rounds up to 80 included
84.999… rounds to 80
85 rounds up to 90 not included
75 ≤ x < 85
step 3 of 4
Decimal places
1. Rounded to tenths: half a tenth is 0.05.
2. Subtract it and add it.
✓ Same method for any accuracy
3.4 to 1 d.p.
one tenth ÷ 2 = 0.05
3.4 − 0.053.4 + 0.05
3.35 ≤ x < 3.45
step 4 of 4
Truncated is different
1. Truncating chops digits off.
2. So the number was 3.4-something.
✓ Starts at the number itself
3.4 truncated to 1 d.p.
3.41, 3.47, 3.499 all chop to 3.4
3.4 ≤ x < 3.5
error intervals —
Half a unit
below and above
≤ then <
lower included, upper not
Truncated
starts at the number itself
Bounds in a calculation (Higher):
biggest ÷ smallest gives the maximum.
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