Rounding
Rounding swaps an exact number for a tidy nearby one that is easier to say, remember and
work with. If a bag holds 47 sweets, it is quicker to say
"about 50". You lose a little exactness, but you gain a number
your brain can hold onto.
To round a whole number to the nearest 10, find the two
tens
it sits between and ask which one it is closer to. Every two-digit number
lives between a "lower ten" and an "upper ten" — for example 47
lives between 40 and 50 — and rounding
just picks the nearer end.
Shopkeepers round all the time. If three toys cost 19,
32 and 48 coins, you don't need the
exact total to know it's "about 20 + 30 + 50 = 100". Rounding
first lets you estimate in your head and check whether an answer is sensible —
a super-power for spotting silly mistakes.
See it on the number line
A number line makes "closer" easy to see. Mark the two tens at the ends, mark the
midpoint halfway between them, then look at where your number sits. If it
lands to the right of the middle it is nearer the upper ten; to the left,
nearer the lower ten.
Press play, then replay it: each time a new two-digit number appears between its two tens,
and you watch it snap to the nearer one.
Try it: which ten is it nearest?
Here is your own number line. A random number appears between two tens with the midpoint
marked. Step it forward to watch it hop to the closer ten, then press Refresh
for a fresh one. Notice how the only thing that matters is which side of the middle the
number is on.
The quick rule: look at the next digit
You don't actually need to draw the line every time. To round to the nearest
10, look only at the ones digit — the digit
just to the right of the tens:
- ones of 0,1,2,3,4 → round down (keep the lower ten).
- ones of 5,6,7,8,9 → round up (go to the next ten).
That single digit decides everything. 5 or more rounds up; 4 or less rounds down.
A 5 in the ones place is exactly halfway between the two tens, and
by convention we always round it up: 25 becomes
30, and 65 becomes
70.
Two traps that catch everyone:
- A 5 in the ones place rounds UP by
convention, never down — 45 rounds to
50, not 40.
- For the nearest ten, look only at the ones digit. To round
47 you check the 7 and get
50 — don't be distracted by the 4
in the tens place.
Three worked examples
- 23 to the nearest 10. Ones digit is
3 (4 or less) → round down. 23 \to 20.
- 68 to the nearest 10. Ones digit is
8 (5 or more) → round up. 68 \to 70.
- 85 to the nearest 10. Ones digit is exactly
5 → halfway, so round up. 85 \to 90.
Rounding to the nearest 100
The same idea scales up. To round to the nearest 100, find the two
hundreds the number sits between and pick the closer one. Now the deciding digit is the
tens digit:
- 347 sits between 300 and
400; the tens digit is 4 → round
down to 300.
- 380 sits between the same two hundreds; the tens digit is
8 → round up to 400.
- 6500 is exactly halfway to the nearest
1000, so it rounds up to 7000.
A stall has 312 apples, 289 oranges
and 97 bananas. Rounded to the nearest hundred that's about
300 + 300 + 100 = 700 pieces of fruit. The real total is
698 — so close to the estimate that rounding gave you a
trustworthy answer in seconds, no adding the long way needed.
Khan Academy walks through rounding to the nearest ten here: