Rounding and comparing

Rounding isn't a magic rule. It answers a real question: which nearby round number is this closest to? $68$ sits between $60$ and $70$ , and it's closer to $70$ .

68 is 2 away from 70 and 8 away from 60.

The rule you learn in school is just a shortcut for that picture. The digit to the right tells you whether you've passed the halfway point.

Look only at the digit right next to the place you're rounding to. 5 or more goes up. 4 or less stays.

Work through it

Round $3, 482$ to the nearest hundred.

Find the two hundreds it's between. $3, 400$ and $3, 500$

Look at the digit right after the hundreds place. It's 8, which is past halfway.round up

Change the rest to zeros. $3, 500$

Round $2, 961$ to the nearest hundred.

The hundreds digit is 9 and the next digit is 6.round up

Nine hundreds plus one more is ten hundreds, so it carries into the thousands. $3, 000$

Which is greater: $4, 098$ or $4, 102$ ?

Compare from the left, one place at a time. Thousands match. $4 = 4$

Hundreds: 0 against 1. The first difference decides, no matter what comes later. $4, 102$ is greater

Watch out for this

Rounding $247$ to the nearest hundred by first rounding 7 up, then 5 up, to get $300$ .

Don't round in a chain. $247$ is closer to $200$ . Look only at the tens digit, 4, which says stay.

The short version
Find the place you're rounding to and look one digit to its right. 5 or more rounds up. 4 or less keeps the digit.

Your turn

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