Which hundred is nearer?
Rounding to the nearest hundred asks the same question as rounding to the nearest ten, one place further left. 347 lies between two hundreds, 300 and 400. It is 47 away from 300 and 53 away from 400, so 300 is the nearer hundred.
Halfway between 300 and 400 is 350. Every number below 350 is nearer to 300, and every number from 350 up is nearer to 400. 347 is below 350, so to the nearest hundred it rounds down to 300.
347 is below the halfway mark of 350, so it rounds down to 300.
The tens digit decides
For the nearest hundred, the tens digit says which side of the halfway mark a number is on. A tens digit of 5 or more rounds up, and 4 or less rounds down. 347 has 4 tens, so it rounds down.
The ones digit does not matter. 349 also rounds down to 300, because 349 is still below 350. Do not round twice: rounding 349 to 350 first and then up to 400 is wrong, because 349 was never past the halfway mark.
To the nearest thousand
For the nearest thousand, move one more place left. 3600 lies between 3000 and 4000, and halfway between them is 3500. 3600 is above 3500, so it is nearer to 4000 and rounds up.
The hundreds digit decides this time: 3600 has 6 hundreds, which is 5 or more. Every digit after the thousands becomes 0, so the answer is 4000.
3600 is above the halfway mark of 3500, so it rounds up to 4000.
Exactly halfway
2500 lies exactly halfway between 2000 and 3000: it is 500 from each. Neither thousand is nearer, and the rule is the one used for tens: a number exactly halfway rounds up. So 2500 rounds to 3000.
One less is different. 2499 is below the halfway mark, so it rounds down to 2000, even though its last two digits are 9s. For the nearest thousand, the hundreds digit decides, and it is 4.
2500 is on the halfway mark, so it rounds up to 3000.
Look one place to the right
Find the place you are rounding to, then look at the digit just to its right. For the nearest hundred it is the tens digit, and for the nearest thousand it is the hundreds digit. Looking at the ones digit instead rounds to the nearest ten, which is a different question.
Take care when the hundreds digit is a 9. 3960 lies between 3900 and 4000, because the hundred after 3900 is 4000. Its tens digit is 6, so to the nearest hundred it rounds up to 4000.
3960 is above the halfway mark of 3950, so it rounds up to 4000.
Worked example: The Halfway Number and the Number Just Before It
Question Farm A has 2499 chickens and Farm B has 2500 chickens. Each number is rounded to the nearest thousand. (a) What is the rounded number for Farm A? (b) What is the rounded number for Farm B?
1.Both numbers are between 2000 and 3000. The halfway number is 2500.
Both numbers are between 2000 and 3000. The halfway number is 2500. 2.2499 is less than the halfway number, so it is nearer to 2000. Round down.
(a) 2499 is below the halfway number, so it rounds down to 2000. 3.(a) For Farm A, 2499 rounds to 2000.
(a) 2499 is below the halfway number, so it rounds down to 2000. 4.2500 is exactly halfway. It is 500 from 2000 and 500 from 3000. The rule is that a halfway number rounds up.
2500 is 500 from each end. A halfway number rounds up. 5.(b) For Farm B, 2500 rounds to 3000.
(b) 2500 rounds up to 3000.
Answer: (a) 2000; (b) 3000
Common mistakes
- Rounding 2500 down to 2000 because it is not nearer to 3000. It is not nearer to 2000 either, and the rule for a halfway number is to round up.
- Rounding 2499 up because its last digits are 9 and 9. For the nearest thousand the hundreds digit decides, and the hundreds digit is 4.
Worked example: A Crowd Reported to the Nearest Hundred
Question A newspaper says that about 3400 people watched a football match. The number was rounded to the nearest hundred. (a) What is the smallest possible number of people? (b) What is the largest possible number of people?
1.Mark 3400 on a number line, with 3300 and 3500 on either side.
Each small mark is 10. The numbers nearest to 3400 round to 3400. 2.Halfway between 3300 and 3400 is 3350. A halfway number rounds up, so 3350 rounds to 3400. The number before it, 3349, rounds down to 3300.
(a) The halfway number 3350 rounds up, so it is the smallest number that rounds to 3400. 3.(a) The smallest possible number of people is 3350.
4.Halfway between 3400 and 3500 is 3450. It rounds up to 3500, so the largest number that still rounds to 3400 is one less: 3450 − 1 = 3449.
From 3350 to 3449, every number rounds to 3400. 5.(b) The largest possible number of people is 3449.
(b) 3449 is the largest. The next number, 3450, rounds up to 3500.
Answer: (a) 3350; (b) 3449
Common mistakes
- Giving 3450 as the largest number. 3450 is a halfway number, and a halfway number rounds up, so 3450 rounds to 3500.
- Giving 3400 as the smallest number. Numbers below 3400 can round up to it. The smallest of them is the halfway number 3350.