Approximation & estimation · Ages 12–13
Rounding off to a place value
Look at the one digit after the place you keep: 5 or more rounds up.
How to do it
Method
Look at the one digit after the place you keep: 5 or more rounds up
3,462 to the nearest hundred: 6 follows, so 3,500
Another way
Halfway on a number line
Halfway between 3,400 and 3,500 is 3,450; 3,462 is nearer 3,500
In full
Rounding off: find the place you keep and look at the one digit to its right. 0 to 4: drop it, and the kept place stays. 5 to 9: round up, and the kept place goes up by 1. Places dropped in the whole-number part become 0: 3,462 to the nearest hundred has 4 in the hundreds and 6 after it, so it rounds up to 3,500. Rounding up can carry: 3,962 to the nearest hundred is 4,000. Or use a number line: 3,462 lies between 3,400 and 3,500, whose halfway mark is 3,450; it is right of halfway, so nearer 3,500. A number exactly halfway goes up: 3,450 to the nearest hundred is 3,500.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
2,785 correct to the nearest ten is 2,790.
True or false?
Show the answer and working
Answer: True
The ones digit is 5: 5 or more rounds up, 4 or less drops. So 2,790.
Example 2
250,527 correct to the nearest thousand is .
Show the answer and working
Answer: 251,000
250,527 lies between 250,000 and 251,000, with 250,500 halfway: it is nearer 251,000. Or look at the hundreds digit.
Example 3
6.05 correct to the nearest whole number is .
Show the answer and working
Answer: 6
Look at the first decimal place, 0: 5 or more rounds up, otherwise it drops. So 6.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.9,122 correct to the nearest ten is .
Answer:
2.5,619 to the nearest hundred: the hundreds digit is , the digit after it is , so the answer is .
Fill in each blank
Answer:
3.2,154 correct to the nearest ten is 2,160.
True or false?
Answer:
4.74.38 correct to the nearest whole number is .
Answer:
5.A whole number is 420 to the nearest ten. It could be 420.
True or false?
Answer:
All the answers
- 1. 9,120
- 2. 6, 1, 5,600
- 3. False
- 4. 74
- 5. True
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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