B. Number · Number Sense: Numbers to 1000 and Fractions

Rounding to the Nearest Ten and Hundred

B1.3About 35 minutes

Learning goals

I can round a number to the nearest ten.
I can round a number to the nearest hundred.
I can use a number line to show which ten or hundred is closer.
I can tell when rounding is useful and when we need an exact number.

Words to know

round
To change a number to a nearby "friendly" number that is easier to use, like a ten or a hundred.

nearest ten
The multiple of ten that is closest, like 350 for 347.

nearest hundred
The multiple of a hundred that is closest, like 300 for 347.

halfway
Exactly in the middle. 345 is halfway between 340 and 350.

about
Close to, but not exact. "About 400 people" might mean 382 people.

Remember from Grade 2

In Grade 2, when you estimated, you found the closest ten to a number, like 30 for 34. This year we call that rounding, and you will also round to the nearest hundred.

About 400 people

The town newspaper says: "About 400 people came to the winter carnival." The real count was 382.

Why didn't the newspaper say 382? Because "about 400" is easier to say, read and remember, and it is close enough. That is rounding.

Rounding to the nearest ten

Find the two tens the number is between.
Decide which ten is closer.

347 is between 340 and 350. It is 7 away from 340 but only 3 away from 350. So 347 rounds to 350.

347 is between 340 and 350. It is closer to 350, so 347 rounded to the nearest ten is 350.

What about halfway?

345 is exactly halfway between 340 and 350. It isn't closer to either one. Mathematicians agreed on a rule: when a number is exactly halfway, round up. So 345 rounds to 350.

A handy shortcut

To round to the nearest ten, look at the ones digit.

0, 1, 2, 3, 4: round down to the ten below (keep the tens digit).
5, 6, 7, 8, 9: round up to the next ten.

But always remember why: you are finding the closer ten.

Worked example

Example 1: Round to the nearest ten

Round 263 to the nearest ten.

263 is between 260 and 270.
The ones digit is 3. 263 is 3 away from 260 and 7 away from 270.
260 is closer.

263 rounds to 260.

Worked example

Example 2: Crossing a hundred

Round 598 to the nearest ten.

598 is between 590 and 600.
It is only 2 away from 600.
Rounding up from 590 goes to the next ten, which is 600.

598 rounds to 600.

Rounding to the nearest hundred

Find the two hundreds the number is between.
The halfway point is the number that ends in 50.
Below halfway: round down. Halfway or above: round up.

347 is between 300 and 400. Halfway is 350. 347 is less than 350, so it rounds down to 300.

347 is between 300 and 400. Halfway is 350. 347 is before halfway, so 347 rounded to the nearest hundred is 300.

Worked example

Example 3: Same number, two answers

Round 347 to the nearest ten and to the nearest hundred.

Nearest ten: 347 is between 340 and 350. It is closer to 350.
Nearest hundred: 347 is between 300 and 400. It is below halfway (350), so it rounds to 300.

Nearest ten: 350. Nearest hundred: 300. Always check which one the question asks for!

Worked example

Example 4: Exactly halfway

Round 650 to the nearest hundred.

650 is between 600 and 700.
650 is exactly halfway.
When a number is halfway, we round up.

650 rounds to 700.

Number	Nearest ten	Nearest hundred
347	350	300
652	650	700
815	820	800
96	100	100
449	450	400
750	750	800

Rounding the same numbers two ways.

Worked example

Example 5: When should we round?

Should you round these numbers? (a) 487 books read by the school in a month. (b) Your phone number. (c) Your house number.

(a) To tell someone about the reading month, "about 500 books" is helpful. Round.
(b) A phone number is a label. Changing it would call the wrong person! Don't round.
(c) A house number is a label too. Rounding would send a visitor to the wrong house. Don't round.

Round when "about" is good enough. Don't round labels, or when you need an exact amount.

Just for fun

Why do numbers that end in 5 always round up?

They are optimists! (Really, it is just the rule mathematicians agreed on.)

Hands-on activity

Book rounding

You need: 6 books from your home or library, paper and a pencil.

For each book, find the number of pages (look at the last page number).
Make a chart with 3 columns: Pages, Nearest ten, Nearest hundred.
Round each page count both ways. Draw a quick number line if you need to.
Which book has about 100 pages? Which has about 300?
Bonus: draw a "rounding hill" with 300 at the bottom left, 350 at the top and 400 at the bottom right. Put a counter on 347. Which way would it roll?

Math talk: "Which ten (or hundred) is my number closer to? How do I know?"

Your turn

Round 74 to the nearest ten.

Round 238 to the nearest ten.

Round 415 to the nearest ten.

Round 382 to the nearest hundred.

Round 549 to the nearest hundred.

Round 850 to the nearest hundred.

A book has 196 pages. About how many pages is that, to the nearest hundred?

More practice: warm-up

Is 43 closer to 40 or to 50?

Round 68 to the nearest ten.

230 is between which two hundreds?

What number is halfway between 600 and 700?

Round 710 to the nearest hundred.

More practice: on your own

Round 995 to the nearest ten.

Jake says 462 rounded to the nearest hundred is 460. Is he right?

Round 307 to the nearest ten and to the nearest hundred.

Should you round your house number when you tell a friend where you live? Why?

638 people came to the fall fair. The newspaper said "about 600". Did they round to the nearest ten or hundred? Were they correct?

Challenge

List all the whole numbers that round to 40 when you round to the nearest ten.

What is the least whole number that rounds to 500 (nearest hundred)? The greatest?

A number rounds to 250 to the nearest ten, and to 300 to the nearest hundred. What could it be?

Check your understanding

Quiz

Round 67 to the nearest ten.

Round 432 to the nearest hundred.

Round 355 to the nearest ten.

Round 750 to the nearest hundred.

Which number rounds to 600 when rounded to the nearest hundred?

When should you NOT round?

For parents and teachers

Big idea: Rounding means finding the nearest "friendly" ten or hundred. Children should understand it as closeness on a number line, not just a rule about digits. The curriculum (B1.3) asks Grade 3 students to round whole numbers to the nearest ten or hundred in various contexts. Rounding is also used for estimating sums and differences in the Operations unit.

Common difficulties:

Mixing up nearest ten and nearest hundred (462 → 460 when the hundred was asked).
Looking at the wrong digit. For the nearest hundred, look at the tens digit, not the ones.
Crossing a hundred or a thousand (598 → 600, 995 → 1000).
Halfway numbers. By convention, halfway rounds up.
Rounding labels such as house or phone numbers.

How to help: Use a quick number line drawing for every question at first. At the store, round prices to the nearest ten dollars. Ask "About how many?" questions: pages in a book, people at a game, kilometres on a trip.