Lesson 29: Rounding Whole Numbers, Rounding Mixed Numbers, Estimating Answers

New Concept

Rounding simplifies numbers to specific place values, making them easier to work with. This skill is used for estimating answers to arithmetic problems.

What’s next

Next, we'll walk through worked examples. You'll learn to round whole numbers, mixed numbers, and estimate answers for various arithmetic problems.

Property

1. If the circled digit is 5 or more, we add 1 to the underlined digit. If the circled digit is less than 5, we leave the underlined digit unchanged.
2. We replace the circled digit and all digits to the right of the circled digit with zeros.

Examples

Round 472 to the nearest hundred:

Explanation

Find the digit you're rounding, then peek at its neighbor to the right. If that neighbor is 5 or more, your digit rounds up before its neighbors turn to zero. If it's 4 or less, it stays put! It’s a trick to find the closest 'tidy' number.

Property

If the fraction is greater than or equal to $\frac{1}{2}$, the mixed number rounds up to the next whole number. If the fraction is less than $\frac{1}{2}$, the mixed number rounds down.

Examples

Round $14 \frac{7}{12}$ to the nearest whole number. Half of 12 is 6. Since $7 > 6$, we round up to 15.
Round $8 \frac{2}{5}$ to the nearest whole number. Half of 5 is 2.5. Since $2 < 2.5$, we round down to 8.
Round $9 \frac{5}{10}$ to the nearest whole number. Since the fraction $\frac{5}{10}$ is equal to $\frac{1}{2}$, we round up to 10.

Explanation

Check the fraction! If the top number is half or more of the bottom number, you’re past the halfway point, so round the whole number up. If it's less than half, the whole number stays the same. It's a quick check to see which whole number is closer.