Lesson 1.3 · Place Value
Rounding multi-digit numbers
A news report might say "about 50,000 fans came to the game" when the exact count was 46,382. Rounding big numbers makes them easier to say, remember and compare. In third grade you rounded to the nearest ten and hundred. Now you can round to any place.
Rounding on a number line
Round 46,382 to the nearest thousand. First find the two thousands it sits between: 46,000 and 47,000. The halfway point is 46,500.
46,382 comes before 46,500, so it is closer to 46,000. It rounds to 46,000.
Now round the same number to the nearest ten thousand. It sits between 40,000 and 50,000, and the halfway point is 45,000.
This time it is past halfway, so it rounds to 50,000. The same number can round to different answers depending on the place you round to.
The rounding rule
You don't need to draw a number line every time. The digit just to the right of the rounding place tells you what to do.
Rounding to any place
- Find the digit in the place you are rounding to. Underline it.
- Look at the digit just to its right.
- If that digit is 5 or more, add 1 to the underlined digit. If it is 4 or less, keep the underlined digit the same.
- Change every digit to the right of the underlined digit to 0.
Worked example: Round to the nearest hundred thousand
Round 739,501 to the nearest hundred thousand.
- The hundred thousands digit is 7.
- The digit to its right (ten thousands) is 3.
- 3 is 4 or less, so the 7 stays.
- Change the rest to zeros.
739,501 rounds to 700,000.
Worked example: Round to the nearest ten thousand
Round 284,690 to the nearest ten thousand.
- The ten thousands digit is 8.
- The digit to its right (thousands) is 4.
- 4 is 4 or less, so the 8 stays.
- The digits after it become zeros.
284,690 rounds to 280,000.
When a 9 rounds up
Sometimes the digit you need to add 1 to is a 9. Then it becomes 10, and you regroup, just like in addition.
Worked example: Rounding up past a 9
Round 396,512 to the nearest ten thousand.
The ten thousands digit is 9. The digit to its right is 6, so you round up.
Nine ten thousands plus one more makes ten ten thousands, which is the same as 1 hundred thousand. So the 3 hundred thousands become 4 hundred thousands, the ten thousands digit becomes 0, and every digit after it becomes 0. The answer is 400,000.
Check: 396,512 is between 390,000 and 400,000, and it is past the halfway point, 395,000. So 400,000 is right.
Common mistake
Only look at the one digit just to the right of the rounding place. To round 44,500 to the nearest thousand, look at the hundreds digit, 5, and round up to 45,000. To round it to the nearest ten thousand, look at the thousands digit, 4, and round down to 40,000. Don't "chain" the rounding by first rounding to 45,000 and then to 50,000.
Tip
Check that your answer makes sense: a rounded number should be close to the original. If you round 62,817 to the nearest thousand, your answer should be 62,000 or 63,000. It can't be 60,000 or 70,000.
Practice
Round 8,462 to the nearest hundred.
Type a number.
Round 23,719 to the nearest thousand.
Type a number.
Round 65,049 to the nearest ten thousand.
Type a number.
Round 451,288 to the nearest hundred thousand.
Type a number.
Round 47,950 to the nearest hundred.
Type a number.
Which number rounds to 30,000 when you round to the nearest ten thousand?
Round 999,500 to the nearest thousand.
Type a number.
The number of people at a fair, rounded to the nearest thousand, is 72,000. What is the smallest whole number of people that could have been there?
Type a number.