Lesson 5 of 8 · Grades 4 to 5
Rounding whole numbers
Rounding trades an exact number for a nearby number that is easier to say and easier to use. To round well you only need two things: the two neighbours the number sits between, and the digit that decides which neighbour wins.
Two neighbours
Rounding replaces a number with a nearby number that is simpler to use. First find the two neighbours the number sits between. To round 2,486 to the nearest ten, the neighbours are 2,480 and 2,490. The exact number is somewhere in that gap, and you have to choose one end.
The deciding digit
One digit makes the decision: the digit one place to the right of the place you are rounding to. When rounding to the nearest ten, look at the ones digit. When rounding to the nearest hundred, look at the tens digit. When rounding to the nearest thousand, look at the hundreds digit.
The rule has two halves. If the deciding digit is 0, 1, 2, 3 or 4, the number rounds down and the place you are rounding to stays the same. If the deciding digit is 5, 6, 7, 8 or 9, the number rounds up and that place grows by one. Five is included in the round-up team, which keeps the rule simple.
Hundreds and thousands
The same number can round to different answers depending on the place. Take 2,486. To the nearest ten it is 2,490, because the ones digit 6 rounds up. To the nearest hundred it is 2,500, because the tens digit 8 rounds up. To the nearest thousand it is 2,000, because the hundreds digit 4 stays put. All three answers are correct; the question says which place to use.
Exactly halfway
A number is exactly halfway when the deciding digit is 5 and all the digits after it are zero. The number 1,250 is exactly halfway between 1,200 and 1,300. The rule sends halfway numbers up, so 1,250 rounds to 1,300. The same happens with 47, which is halfway between 40 and 50 and rounds up to 50.
Watch out for this
Read the deciding digit in the correct place. To round 6,499 to the nearest thousand, look at the hundreds digit, which is 4. The answer is 6,000, not 7,000. The 9 in the tens place is loud, but it has no vote for the thousands place. Only the digit one place to the right decides.
When rounding helps
Rounding is useful for quick estimates. A book with 287 pages has about 290 pages to the nearest ten, and a shop with 398 customers had about 400 customers to the nearest hundred. The rounded number is not exact, so say "about" when you use it.
Worked example
Round 2,486 to the nearest ten, the nearest hundred and the nearest thousand.
Step 1: nearest ten. The two neighbours are 2,480 and 2,490. The ones digit is 6, so round up to 2,490.
Step 2: nearest hundred. The neighbours are 2,400 and 2,500. The tens digit is 8, so round up to 2,500.
Step 3: nearest thousand. The neighbours are 2,000 and 3,000. The hundreds digit is 4, so stay at 2,000.
Step 4: check that each answer is a valid neighbour and that the deciding digit was read in the right place.
Answer: 2,490 to the nearest ten, 2,500 to the nearest hundred and 2,000 to the nearest thousand.
Remember
- Find the two neighbours around the number.
- The deciding digit sits one place to the right.
- 0 to 4 rounds down; 5 to 9 rounds up.
- A number exactly halfway always rounds up.
Try it
Answer the five questions below. Work them out first, then open each answer to check.
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Round 47 to the nearest ten.
Show answer
50. The ones digit is 7, so the number rounds up.
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Round 632 to the nearest hundred.
Show answer
600. The tens digit is 3, so the hundreds digit stays.
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Round 4,512 to the nearest thousand.
Show answer
5,000. The hundreds digit is 5, so the number rounds up to the next thousand.
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Round 1,250 to the nearest hundred.
Show answer
1,300. It is exactly halfway, and the rule sends halfway numbers up.
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A school has 398 students. About how many is that, to the nearest hundred?
Show answer
400 students. The tens digit is 9, so 398 rounds up.
Puzzle · Rounding riddle
Puzzle time
I am a whole number. Rounded to the nearest thousand I am 2,000. Rounded to the nearest hundred I am 1,900. Which number am I?
Show a hint
The number must be at least 1,850 and less than 1,950. Then check which option is closest to 1,900.
Show the answer
Answer: 1,851. 1,851 is between 1,850 and 1,950, and it rounds to 1,900 to the nearest hundred. 1,849 rounds to 1,800, and the other two round to 2,000.