Lesson 6: Rounding Multi-Digit Numbers to Any Place Value

Property

To round a number to the nearest thousand, first find the nearest lower thousand and the nearest higher thousand. The midpoint is the number in the middle between them.

• The upper thousand is $1000$ more than the lower thousand:

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To round a number to the nearest thousand, plot it on a vertical number line. If the number is less than the midpoint, round down to the lower thousand. If the number is greater than or equal to the midpoint, round up to the upper thousand.

Examples

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When rounding to the nearest thousand, a number that is exactly at the midpoint between two thousands always rounds up to the greater thousand. The midpoint is found by adding 500 to the lower thousand.

Examples

Property

How to round a whole number to a specific place value:

1. Locate the given place value.
2. Underline the digit to the right of the given place value.
3. Determine if this digit is greater than or equal to 5.
   • Yes: add 1 to the digit in the given place value. Handle any regrouping (like 9 becoming 10).
   • No: do not change the digit in the given place value.
4. Replace all digits to the right of the given place value with zeros.

Examples

• To round $4,862$ to the nearest hundred, look at the tens digit (6). Since $6 \ge 5$, round up the hundreds digit. The result is $4,900$.
• Rounding $12,345$ to the nearest thousand means looking at the hundreds digit (3). Since $3 < 5$, the thousands digit stays the same. The result is $12,000$.
• Rounding $49,850$ to the nearest thousand involves looking at the hundreds digit (8). Since $8 \ge 5$, we add 1 to the 9, which requires regrouping. The result is $50,000$.

Explanation

Rounding simplifies a number. Look at the digit just to the right of the place you're rounding to. If that digit is 5 or more, you round up. If it's 4 or less, you keep the digit the same.