Rounding Natural Numbers

Rounding replaces a number with a nearby "round" number that is easier to work with. Learn to round to the nearest 10, 100, 1 000, and 10 000.

What Is Rounding?

Rounding means replacing a number with a simpler number that is close to the original. The result is called an approximation — it is not exact, but it is good enough for many situations.

We round to a specific place value: the nearest 10, 100, 1 000, or 10 000.

Note

The symbol $\approx$ means "approximately equal to". For example: $4\,763 \approx 5\,000$ (rounded to the nearest thousand).

The Rounding Rule

\text{digit to the right} \geq 5 \Rightarrow \text{round up} \quad;\quad \text{digit to the right} < 5 \Rightarrow \text{round down}

Look at the digit immediately to the right of the rounding position. 5 or more: round up. 4 or less: round down.

This is sometimes called the "5 and above — round up" rule.

Rounding to the Nearest 10

To round to the nearest 10, look at the units digit.

If it is 0, 1, 2, 3, or 4 — round down (keep the tens digit, set units to 0)
If it is 5, 6, 7, 8, or 9 — round up (increase tens digit by 1, set units to 0)

1
Identify the units digit
This is the digit in the ones place — the last digit.
2
Apply the rule
Is the units digit 5 or more? Round up. Less than 5? Round down.
3
Replace all digits to the right with zeros
The units digit becomes 0.

Round 347 to the nearest 10

The units digit is 7 (which is ≥ 5), so round up.

$347 \approx 350$

Round 2 342 to the nearest 10

The units digit is 2 (which is < 5), so round down.

$2\,342 \approx 2\,340$

Rounding to the Nearest 100

Look at the tens digit.

Round 4 763 to the nearest 100

The tens digit is 6 (which is ≥ 5), so round up.

$4\,763 \approx 4\,800$

Round 12 430 to the nearest 100

The tens digit is 3 (which is < 5), so round down.

$12\,430 \approx 12\,400$

Rounding to the Nearest 1 000

Look at the hundreds digit.

Round 38 600 to the nearest 1 000

The hundreds digit is 6 (which is ≥ 5), so round up.

$38\,600 \approx 39\,000$

Round 5 249 to the nearest 1 000

The hundreds digit is 2 (which is < 5), so round down.

$5\,249 \approx 5\,000$

Rounding to the Nearest 10 000

Look at the thousands digit.

Round 274 300 to the nearest 10 000

The thousands digit is 4 (which is < 5), so round down.

$274\,300 \approx 270\,000$

Round 185 700 to the nearest 10 000

The thousands digit is 5 (which is ≥ 5), so round up.

$185\,700 \approx 190\,000$

Summary Table

Round to nearest	Look at	Example	Result
10	units digit	347	350
100	tens digit	4 763	4 800
1 000	hundreds digit	38 600	39 000
10 000	thousands digit	274 300	270 000

Real-World Examples

Real world: rounding prices

A pair of trainers costs 87 €. Rounded to the nearest 10 €, that is approximately 90 €. This is useful when estimating whether you have enough money before checking the exact price.

Real world: rounding distances

The distance between two cities is 3 748 km. Rounded to the nearest 1 000 km, that is approximately 4 000 km — a much easier number to remember and discuss.

Real world: population estimates

A region has a population of 486 250 people. News reports often round this:

To the nearest 1 000: 486 000
To the nearest 10 000: 490 000
To the nearest 100 000: 500 000

Larger rounding = simpler number but less precise.

Real world: estimating a total bill

A shopping cart has items costing 143 €, 67 €, and 289 €. Before calculating exactly, you can round each to the nearest 10: $140 + 70 + 290 = 500$ €.

The exact total is 499 €, so the estimate is very close!

Common Mistakes

Looking at the wrong digit — always look at the digit to the RIGHT of where you are rounding to
Forgetting to replace all digits to the right with zeros after rounding up or down
Rounding 9 up and forgetting that it carries over (e.g. 4 950 rounded to nearest 100 → look at tens digit 5 → round up → 5 000, not 4 900)
Confusing "round to the nearest 10" with "round to the tens digit" — they mean the same thing, but students sometimes look at the tens digit instead of the units digit
Thinking that rounding always gives a smaller number — rounding up gives a larger number!

Tip

When a 9 rounds up and causes a chain of carries (e.g. 3 996 rounded to the nearest 10 → 4 000), take it step by step: 6 ≥ 5, round up the tens → 3 996 becomes 4 000.

Practice Problems

Round 6 482 to the nearest 100.

Show answer

Look at the tens digit: 8 ≥ 5, so round up. 6 482 ≈ 6 500.

Round 73 450 to the nearest 1 000.

Show answer

Look at the hundreds digit: 4 < 5, so round down. 73 450 ≈ 73 000.

A city has 248 630 inhabitants. Round this to the nearest 10 000.

Show answer

Look at the thousands digit: 8 ≥ 5, so round up. 248 630 ≈ 250 000.