Mathematics (Core)Exam code: 0580

Rounding Estimation and Bounds

Number

Locate the digit sitting in the place value being rounded to
Look at the single digit immediately to its right, and ignore everything beyond it
That digit decides the direction: 5 or more rounds up, 4 or less leaves the digit unchanged
Fill every place between the rounded digit and the decimal point with zeros, since dropping them would change the size of the number
- 4826 to the nearest hundred is 4800
- 4872 to the nearest hundred is 4900

Worked example

Rounding to the nearest ten, hundred and thousand

Write 63 948 correct to (a) the nearest ten, (b) the nearest hundred, (c) the nearest thousand.

Solution:

(a) The tens digit is 4, and the digit to its right is 8, which is 5 or more, so the 4 rounds up to 5
63 948 = 63 950 to the nearest ten
(b) The hundreds digit is 9, and the digit to its right is 4, so the 9 stays as it is
63 948 = 63 900 to the nearest hundred, with zeros filling the tens and ones columns
Round 63 948 itself, not the answer to (a): 63 950 rounded to the nearest hundred would give 64 000, which is wrong
(c) The thousands digit is 3, and the digit to its right is 9, so the 3 rounds up to 4
63 948 = 64 000 to the nearest thousand
Every answer keeps the size of the original number: 639 in place of 63 900 would be a hundred times too small

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