Round numbers to the nearest 10, 100 or 1000
Theory
Rounding numbers to the nearest 10, 100 or 1000 is a Year 4 skill: swapping a number for a tidy nearby number that is easier to use. This Year 4 maths page shows how to check the digit to the right of the rounding place, use a number line, deal with halfway numbers, round prices, distances and crowds, and work backwards to find which numbers round to a given value. Curriculum: VC2M4N07 / AC9M4N07.
Rounding means replacing a number with a nearby tidy number that is easier to say and work with. When you round, you land on a multiple of 10, 100 or 1000, like 50, 600 or 4000.
To round, look at the digit just to the right of the place you want. For the nearest 10 check the ones digit, for the nearest 100 check the tens digit, and for the nearest 1000 check the hundreds digit. If that digit is 4 or less you round down; if it is 5 or more you round up.
The halfway number sits exactly between two tidy numbers, like \(35\) between \(30\) and \(40\). A number that is exactly halfway always rounds up, so \(35\) rounds to \(40\).
Rounding does not need a formula. This table shows which digit to check.
| Round to the nearest… | Check this digit | 0–4 | 5–9 |
|---|---|---|---|
| 10 | ones | round down | round up |
| 100 | tens | round down | round up |
| 1000 | hundreds | round down | round up |
How to round to the nearest 10, 100 or 1000
- Find the rounding place. Decide whether you want the nearest 10, 100 or 1000, and point to that digit.
- Look one place to the right. For the nearest 10 that is the ones digit, for the nearest 100 the tens digit, and for the nearest 1000 the hundreds digit.
- Decide up or down. If that digit is 4 or less, keep the rounding place the same. If it is 5 or more, add one to the rounding place. Then fill every place after it with zeros.
How to use a number line
- Mark the two tidy numbers on each side of your number and the halfway point between them.
- See which side it is on. Left of halfway rounds down, right of halfway (or exactly on it) rounds up.
How to work backwards
- Find the smallest number: it is the halfway number below, because halfway rounds up.
- Find the largest number: it is one less than the halfway number above.
| \(\text{ones digit}\) | \(=\) | \(7\) |
| \(7\) | \(\ge\) | \(5 \Rightarrow \text{round up}\) |
| \(47\) | \(\to\) | \(50\) |
7 is 5 or more, so 47 rounds up to \(50\).
| \(\text{tens digit}\) | \(=\) | \(8\) |
| \(8\) | \(\ge\) | \(5 \Rightarrow \text{round up}\) |
| \(582\) | \(\to\) | \(600\) |
The hundreds digit 5 goes up to 6, so 582 rounds to \(600\).
| \(\text{hundreds digit}\) | \(=\) | \(2\) |
| \(2\) | \(<\) | \(5 \Rightarrow \text{round down}\) |
| \(8200\) | \(\to\) | \(8000\) |
2 is 4 or less, so the thousands digit 8 stays the same: \(8000\).
| \(\text{nearest } 10\) | \(:\) | \(3750\ (\text{ones } 0)\) |
| \(\text{nearest } 100\) | \(:\) | \(3800\ (\text{tens } 5)\) |
| \(\text{nearest } 1000\) | \(:\) | \(4000\ (\text{hundreds } 7)\) |
(i) \(3750\): it is already a multiple of 10.
(ii) \(3800\): the tens digit is 5, so round up.
(iii) \(4000\).
(ii) A crowd of \(52\,371\) people came to a concert. Round it to the nearest 1000.
| \(\$184\) | \(\to\) | \(\$180\ (\text{ones } 4)\) |
| \(\$184\) | \(\to\) | \(\$200\ (\text{tens } 8)\) |
| \(52\,371\) | \(\to\) | \(52\,000\) |
(i) \(\$180\) to the nearest \(\$10\); \(\$200\) to the nearest \(\$100\).
(ii) \(52\,000\): the hundreds digit is 3, so round down.
| \(\text{tens digit}\) | \(=\) | \(6 \Rightarrow \text{round up}\) |
| \(9\text{ hundreds} + 1\) | \(=\) | \(10\text{ hundreds}\) |
| \(2963\) | \(\to\) | \(3000\) |
The 9 hundreds become 10 hundreds, which is one more thousand, so the answer is \(3000\), not \(2900\) or \(21\,000\).
| \(\text{smallest}\) | \(=\) | \(75\) |
| \(\text{largest}\) | \(=\) | \(84\) |
75 is halfway and rounds up; 85 would round up to 90, so 84 is the largest.
| \(\text{smallest}\) | \(=\) | \(350\) |
| \(\text{largest}\) | \(=\) | \(449\) |
(i) \(350\) (halfway rounds up).
(ii) \(449\); \(450\) would round up to \(500\).
Common pitfalls
Frequently asked questions
How do you round to the nearest 10?
Look at the ones digit. If it is 4 or less, round down and keep the tens the same. If it is 5 or more, round up to the next ten. For example, \(47\) rounds to \(50\) and \(73\) rounds to \(70\).
How do you round to the nearest 100?
Look at the tens digit. If it is 4 or less, round down and keep the hundreds the same. If it is 5 or more, round up to the next hundred. For example, \(582\) rounds to \(600\) and \(438\) rounds to \(400\).
How do you round to the nearest 1000?
Look at the hundreds digit. For example, \(8200\) rounds down to \(8000\) and \(5740\) rounds up to \(6000\).
What do you do when a number is exactly halfway?
A number that is exactly halfway always rounds up. To the nearest \(10\), \(35\) rounds up to \(40\). To the nearest \(100\), \(150\) rounds up to \(200\).
What is rounding used for?
Rounding gives a quick, tidy estimate. It helps you guess a total in your head, check if an answer is sensible, and talk about big amounts, like saying a crowd of \(4820\) people is about \(5000\).
Why does 397 round to 400 to the nearest 10?
The ones digit is \(7\), which is \(5\) or more, so you round up. The tens digit \(9\) becomes \(10\), so it carries into the hundreds and the number becomes \(400\), not \(390\).