Lesson 17: Rounding and Estimating

New Concept

Rounding and estimating are essential tools for finding approximate values. We use them to simplify complex numbers and check if our calculations are reasonable.

What’s next

Next, we will break down the specific rules for rounding. You'll then apply these techniques in worked examples involving whole numbers, decimals, and fractions.

Property

We round a number to a certain place value by inspecting the digit that follows that place. If the digit is 5 or greater we round up. If the digit is less than 5 we round down.

Examples

$1,4\underline{8}1,362 \rightarrow 1,500,000$ (The ten-thousands digit, 8, is greater than 5, so round up).
$5,2\underline{3}4 \rightarrow 5,200$ (The tens digit, 3, is less than 5, so round down).
$7\underline{8} \rightarrow 80$ (The ones digit, 8, is greater than 5, so round up).

Explanation

Simplifying numbers makes them much easier to use! Think of it like finding the nearest 'friendly' number on a number line that ends in zero. If the digit to the right is 5 or more, you power up to the next level. If it's less than 5, you just slide back down. Easy peasy!

Property

To round a decimal, we find a decimal number with fewer decimal places. We inspect the digit to the right of the place we are rounding to and round up for 5 or greater, and down for less than 5.

Examples

Round $3.14\underline{1}59$ to two decimal places: $3.14$.
Round $3.141\underline{5}9$ to four decimal places: $3.1416$.
Round $2.19\underline{9}$ to the nearest hundredth: $2.20$.

Explanation

This is like giving a number a clean haircut! You decide how many decimal places to keep, then peek at the next digit. If that digit is a 5 or bigger, you give the last digit a little boost upwards. If it’s smaller than 5, you simply snip off the extra decimal places for a tidier look.

Property

To round a mixed number to the nearest whole number, we decide if the fraction is more than or less than $\frac{1}{2}$. If the numerator is half or greater than half of the denominator, we round up.

Examples

$13\frac{5}{12} \rightarrow 13$ (Since $5$ is less than half of $12$, we round down).
$4\frac{5}{8} \rightarrow 5$ (Since $5$ is greater than half of $8$, we round up).
$7\frac{3}{6} \rightarrow 8$ (Since $3$ is exactly half of $6$, we round up).

Explanation

Is that fraction a big deal or a little one? Check if the top number is at least half of the bottom number. If it is, you’ve climbed past the halfway point and get to round up to the next whole number! If not, it’s not quite enough, so you just drop the fraction and keep the whole number.