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Rounding a Number

Rounding a Number

A method of approximating a number using a nearby number at a given degree of accuracy.

For example, 3.14159265... rounded to the nearest thousandth is 3.142. That is because the third number after the decimal point is the thousandths place, and because 3.14159265... is closer to 3.142 than 3.141.

 

 

See also

Truncating a number

Worked Example

Problem: Round 4,738 to the nearest hundred.
Step 1: Identify the hundreds digit and the digit immediately to its right.
4,738hundreds digit=7,tens digit=34,\mathbf{7}38 \quad \text{hundreds digit} = 7, \quad \text{tens digit} = 3
Step 2: Apply the rounding rule: if the next digit is 5 or greater, round up; if it is less than 5, round down. Here the tens digit is 3, which is less than 5, so round down.
Step 3: Keep the hundreds digit as 7 and replace all digits to its right with zeros.
4,738≈4,7004,738 \approx 4,700
Answer: 4,738 rounded to the nearest hundred is 4,700.

Why It Matters

Rounding is essential whenever exact values are impractical, such as reporting measurements, estimating costs, or simplifying mental arithmetic. Scientists round data to reflect the precision of their instruments, and everyday tasks like splitting a restaurant bill rely on rounding to the nearest cent or dollar.

Common Mistakes

Mistake: When a digit is exactly 5, students sometimes round down instead of up.
Correction: The standard convention taught in most courses is to round up when the deciding digit is 5. For example, 2.65 rounded to the nearest tenth becomes 2.7, not 2.6.

Related Terms