Lesson 3: Use place value understanding to round multi-digit numbers to any place value.

Property

To round a number, first find the two benchmark numbers (e.g., the two thousands) it is between. Then, find the midpoint. If the number is greater than or equal to the midpoint, round up to the next benchmark. If the number is less than the midpoint, round down to the lower benchmark.

Examples

• To round $36,812$ to the nearest thousand: The number is between $36,000$ and $37,000$. The midpoint is $36,500$. Since $36,812 \geq 36,500$, we round up to $37,000$.
• To round $124,500$ to the nearest ten thousand: The number is between $120,000$ and $130,000$. The midpoint is $125,000$. Since $124,500 < 125,000$, we round down to $120,000$.
• To round $750,000$ to the nearest hundred thousand: The number is between $700,000$ and $800,000$. The midpoint is $750,000$. Since $750,000 \geq 750,000$, we round up to $800,000$.

Explanation

This skill involves rounding larger numbers to a specific place value like the thousands, ten thousands, or hundred thousands. First, you identify the two multiples of that place value that your number falls between. Then, you determine the halfway point, or midpoint, between them. If your number is at or above the midpoint, you round up; otherwise, you round down.

Property

For a number rounded to a specific place value, the smallest possible original number is the midpoint below the rounded value. The largest possible original whole number is one less than the midpoint above the rounded value. If $R$ is the rounded number, the range of possible original whole numbers $N$ is from the lower midpoint to the upper midpoint minus 1.

Examples