Round numbers to any specified place value

Rounding a multi-digit whole number to a specified place value preserves the value of the selected digit while replacing all digits to its right with zeros, based on whether the next digit is less than 5 or at least 5; a number line illustrates the choice of the nearer benchmark multiple. This develops place-value reasoning and estimation, including the distinction between changing a numeral’s form and changing its exact value; decimal, negative-number, and more general real-number rounding are not included.

Detailed Explanation: Round numbers to any specified place value

To round a whole number to a specified place value:

Find the digit in the place you are rounding to.
Look at the digit immediately to its right.
If that digit is less than $5$ , keep the rounding digit the same.
If that digit is $5$ or greater, increase the rounding digit by $1$ .
Change every digit to the right of the rounding digit to $0$ .

Example: Round $47{,}362$ to the nearest hundred.

The hundreds digit is $3$ :

47\boxed{3}62

Look at the digit to its right, the tens digit, which is $6$ .
Since $6$ is at least $5$ , increase the hundreds digit from $3$ to $4$ .
Replace the tens and ones digits with zeros.

So,

47{,}362 \approx 47{,}400

You can also picture this on a number line. The number $47{,}362$ is between $47{,}300$ and $47{,}400$ . It is closer to $47{,}400$ , so $47{,}400$ is the nearest hundred.

Rounding changes the way the number is written to make it easier to use for an estimate. It does not give the exact original value.

Learn by doing: Round numbers to any specified place value

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Rounding Whole Numbers - Thousands to Nearest Hundred

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