Error intervals from rounding

The Maths Habit Handout to print

Which balls will end up in the middle valley?

ABCD

B and C. Every ball between the two tops rolls into the valley.

Error interval
All the numbers that round to the same value.
Lower bound
The smallest number that rounds to the value.
Upper bound
Where the error interval stops. It rounds to the next value, so it is not in the interval.

4.64.74.84.654.75
  1. Put the rounded number in the valley.
  2. The bounds are the two tops.
  3. First top: it rolls into the valley, so it is in. Use ≤.
  4. Second top: it rolls out of the valley, so it is not in. Use <.

Does it end up in the valley?

4.64.74.84.654.75 Yes: it rolls into the valley

Does it end up in the valley?

4.64.74.84.654.75 No: it rolls out of the valley

It is on the first top. Does it end up in the valley?

4.64.74.84.654.75 Yes: it rolls into the valley

It is on the second top. Does it end up in the valley?

4.64.74.84.654.75 No: it rolls out of the valley

x is 4.7 rounded to 1 decimal place. Put it in the valley. The bounds are the two tops. Find them. 4.65 and 4.75

4.64.74.84.654.75rounds to 4.7

x is 6.2 rounded to 1 decimal place. Put it in the valley. The bounds are the two tops. Find them. 6.15 and 6.25

6.16.26.36.156.25rounds to 6.2

x is 4.7 rounded to 1 decimal place. Put it in the valley. The bounds are the two tops. Find them. 4.65 and 4.75

4.64.74.84.654.75rounds to 4.7

x is 3.8 rounded to 1 decimal place. Put it in the valley. The bounds are the two tops. Find them. 3.75 and 3.85

3.73.83.93.753.85rounds to 3.8

x is 4.7 rounded to 1 decimal place. Put it in the valley. The bounds are the two tops. Find them. 4.65 and 4.75

4.64.74.84.654.75rounds to 4.7

x is 9.1 rounded to 1 decimal place. Put it in the valley. The bounds are the two tops. Find them. 9.05 and 9.15

9.19.09.29.059.15rounds to 9.1

x is 4.7 rounded to 1 decimal place. Put it in the valley. The bounds are the two tops. Find them. 4.65 and 4.75

4.64.74.84.654.75rounds to 4.7

x is 7.0 rounded to 1 decimal place. Put it in the valley. The bounds are the two tops. Find them. 6.95 and 7.05

6.97.07.16.957.05rounds to 7.0

x is 4.7 rounded to 1 decimal place. Put it in the valley. The bounds are the two tops. Find them. 4.65 and 4.75

4.64.74.84.654.75rounds to 4.7

x is 12.9 rounded to 1 decimal place. Put it in the valley. The bounds are the two tops. Find them. 12.85 and 12.95

12.812.913.012.8512.95rounds to 12.9

Error intervals from rounding worksheet, page 1

<
Less than.
≤
Less than or equal to.

x is 5.4 rounded to 1 decimal place. Write the error interval for x. 5.35 ≤ x < 5.45

5.35.45.55.355.45
≤ x <

x is 5.4 rounded to 1 decimal place. Write the error interval for x. 5.35 ≤ x < 5.45

5.35.45.55.355.45
≤ x <

x is 6.2 rounded to 1 decimal place. Write the error interval for x. 6.15 ≤ x < 6.25

6.16.26.36.156.25
6.15≤ x <

x is 5.4 rounded to 1 decimal place. Write the error interval for x. 5.35 ≤ x < 5.45

5.35.45.55.355.45
≤ x <

x is 3.48 rounded to 2 decimal places. Write the error interval for x. 3.475 ≤ x < 3.485

3.473.483.493.4753.485
3.475≤ x <

Error intervals from rounding worksheet, page 2

Answer sheet

Does it round to 4.7? Thumbs up: yes. Thumbs down: no.

  1. 4.65

    Yes

  2. 4.75

    No

  3. 4.749

    Yes

  4. 4.64

    No

  5. 4.7

    Yes

  1. An error interval is 2.55 ≤ x < 2.65. What was x rounded to?

    2.6

  2. x is 8 rounded to the nearest whole number. Write the error interval for x.

    7.5 ≤ x < 8.5

  3. x is 0.3 rounded to 1 decimal place. Write the error interval for x.

    0.25 ≤ x < 0.35

  1. x is 5.3 rounded to 1 decimal place. Find the lower bound and the upper bound of x.

    5.25 and 5.35

  2. y is 8.6 rounded to 1 decimal place. Write the error interval for y.

    8.55 ≤ y < 8.65

  3. z is 2.47 rounded to 2 decimal places. Write the error interval for z.

    2.465 ≤ z < 2.475
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