Rounding Formula

The Formula

If the digit to the right of the rounding place is \geq 5, round up; if < 5, round down

When to use: Simplifying for easier calculation or communication—19.87 becomes 'about 20'.

Quick Example

Round 3.14159 to two decimal places: 3.14. Round 847 to nearest hundred: 800.

Notation

\approx is used to show a rounded value; e.g., 3.14159 \approx 3.14

What This Formula Means

Replacing a number with a nearby simpler approximation at a specified place value, using the digit to the right to decide.

Simplifying for easier calculation or communication—19.87 becomes 'about 20'.

Worked Examples

Example 1

easy
Round 4{,}736.482 to (a) the nearest hundred, (b) the nearest tenth.

Solution

  1. 1
    Identify the target place and look at the digit immediately to its right.
  2. 2
    (a) Nearest hundred: The hundreds digit is 7; look at the tens digit: 3 < 5, so round down (keep hundreds digit as 7). 4{,}736.482 \approx 4{,}700.
  3. 3
    (b) Nearest tenth: The tenths digit is 4; look at the hundredths digit: 8 \geq 5, so round up. 4{,}736.482 \approx 4{,}736.5.

Answer

(a) 4{,}700; (b) 4{,}736.5
Rounding uses the digit immediately to the right of the target place: if it is 5 or more, increase the target digit by 1; if it is less than 5, leave the target digit unchanged. All digits to the right then become zero (or are dropped for decimals).

Example 2

medium
Round \pi \approx 3.14159265\ldots to 4 significant figures. Then round 0.0038472 to 3 significant figures.

Common Mistakes

  • Rounding 847 to the nearest hundred as 900 instead of 800 — look at the tens digit (4), which is less than 5, so round down
  • Changing digits to the right of the rounding place to something other than zero — 847 rounded to the nearest hundred is 800, not 850
  • Rounding twice in sequence — rounding 449 to tens gives 450, then rounding 450 to hundreds gives 500, but rounding 449 directly to hundreds gives 400

Why This Formula Matters

Essential for estimation, significant figures, and practical communication.

Frequently Asked Questions

What is the Rounding formula?

Replacing a number with a nearby simpler approximation at a specified place value, using the digit to the right to decide.

How do you use the Rounding formula?

Simplifying for easier calculation or communication—19.87 becomes 'about 20'.

What do the symbols mean in the Rounding formula?

\approx is used to show a rounded value; e.g., 3.14159 \approx 3.14

Why is the Rounding formula important in Math?

Essential for estimation, significant figures, and practical communication.

What do students get wrong about Rounding?

The 'round 5 up' rule: when the deciding digit is exactly 5, round up—e.g., 2.45 rounded to tenths is 2.5.

What should I learn before the Rounding formula?

Before studying the Rounding formula, you should understand: place value.

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