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Rounding to Any Place, and Comparing Two Roundings

Maths · Stage 3
Year 5
Lesson Guide
Explanation
Rounding to the nearest million means asking: which million is this number closest to? For 4 850 000 the two candidates are 4 000 000 and 5 000 000. On the number line it is 850 000 past four million and only 150 000 short of five million, so five million is nearer. That is the whole idea. The shortcut you already know — look at the next digit, five or more goes up — is just a fast way of finding which neighbour is nearer. The 8 in the hundred-thousands tells you the number is more than halfway to the next million.
Your Turn
Round 2 380 000 to the nearest million using the number line in your head. Check: the neighbours are 2 and 3 million; 380 000 is less than halfway, so 2 000 000.
Watch Out
The neighbours are the round numbers on either side, not the digits. Students who round 4 850 000 to "4 800 000" have rounded to the wrong place.
Explanation
Here is the same number rounded three ways. To the nearest million, the deciding digit is the 8 in the hundred-thousands: up, so 5 000 000. To the nearest hundred thousand, the deciding digit is the 5 in the ten-thousands: up, so 4 900 000. To the nearest ten thousand, the deciding digit is the 0 in the thousands: stays, so 4 850 000 — it was already a round number of ten thousands. The method never changes. Find the place, look one digit to its right, let that digit decide, then turn everything to the right into zeros.
Your Turn
Round 63 749 to the nearest thousand, then to the nearest hundred. Check: 64 000 (the 7 decides) and 63 700 (the 4 decides).
Watch Out
Only the digit immediately to the right decides. 63 749 to the nearest thousand looks at the 7, not at the 49. And a 9 that rounds up carries: 39 600 to the nearest thousand is 40 000.
Explanation
Tests like to give one number to two people who round it to different places, then ask how far apart their answers are. Alinta rounds 4 850 000 to the nearest million and gets 5 000 000. Tau rounds the same number to the nearest hundred thousand and gets 4 900 000. The difference is 100 000. The trap is to round one answer from the other — rounding Tau's 4 900 000 to the nearest million also gives 5 000 000, but that is not what the question asked. Do each rounding from the original number, then compare.
Your Turn
Round 267 500 to the nearest hundred thousand and to the nearest ten thousand. What is the difference? Check: 300 000 and 270 000; difference 30 000.
Watch Out
Both roundings start from the ORIGINAL number. The second rounding is not the first one rounded again.
Explanation
Another test favourite: several numbers are rounded to the same place, and you are asked which one changes the most, or the least. The change is the distance between the number and the round number it lands on. 12 499 rounds down to 12 000, a move of 499. 12 500 rounds up to 13 000, a move of 500. 12 940 rounds up to 13 000, a move of only 60. So the biggest change is always the number nearest to halfway, and the smallest is the one that was nearly round already. Work each move out; it takes a subtraction each and there is no way to see it from the size of the numbers.
Your Turn
Which changes more when rounded to the nearest hundred: 3 349 or 3 291? Check: 3 349 → 3 300, moves 49; 3 291 → 3 300, moves 9. So 3 349.
Watch Out
A number that rounds UP can still move less than a number that rounds DOWN. Direction and distance are different things.
Explanation
The everyday use of rounding is checking. Before adding 38 217 and 24 906, round both to the nearest thousand and add in your head: 38 000 and 25 000 make about 63 000. Now do the exact sum and get 63 123. That is close to the estimate, so you can believe it. If you had got 53 123, the estimate would be shouting that a digit went wrong. On a test, ten seconds of estimating catches the slips that cost the most marks. But the estimate is only ever the check: when the question asks for the sum, it wants 63 123.
Your Turn
Estimate 71 480 − 19 620 to the nearest thousand, then work it out exactly. Check: about 71 000 − 20 000 = 51 000; exactly 51 860.
Watch Out
If the question says "estimate", give the rounded answer. If it says "work out" or "calculate", give the exact one. Read which it is.
📌 Key Points — this lesson in a nutshell
  • Rounding asks: which of the two nearest round numbers am I closer to? Find them both, then look at the digit to the right of the place you are rounding to.
  • That digit decides: 0–4 stays, 5–9 goes up. Everything to its right becomes zero.
  • Rounding to a bigger place can change a number more. Rounding 4 850 000 to the nearest million moves it 150 000; to the nearest hundred thousand, only 50 000.
  • A rounded answer is an estimate. Use it to check a calculation, never as the calculation.
Step 1: Introduction
Step 1 of 5
Round 4 850 000 to the nearest million 4 000 0004 500 0005 000 0004 850 000 The two nearest millions are 4 000 000 and 5 000 000. 4 850 000 is 850 000 past 4 million and only 150 000 short of 5 million. Nearest million: 5 000 000 Shortcut: the digit to the right of the millions is 8. It is 5 or more, so round up. The shortcut and the number line always agree — the number line is why the shortcut works.
Same number, rounded to three different places nearest million 4 850 000 → 5 000 000 nearest hundred thousand 4 850 000 → 4 900 000 nearest ten thousand 4 850 000 → 4 850 000 Find the place. Look ONE digit to its right. That digit decides. 0, 1, 2, 3, 4 → the place stays. 5, 6, 7, 8, 9 → the place goes up by one. Then every digit to the right of the place becomes 0. A 5 with nothing after it is exactly halfway — by agreement, halfway goes up.
Alinta rounds to the nearest million; Tau to the nearest hundred thousand 4 800 0004 900 0005 000 000numberTauAlinta Alinta: 4 850 000 → 5 000 000 Tau: 4 850 000 → 4 900 000 Difference: 5 000 000 − 4 900 000 = 100 000 Two roundings of the same number can land in different places. Do each one on its own, then subtract. Never round a rounded answer.
Rounding to the nearest thousand — who moves furthest? numbernearest thousandmoved by 12 49912 000499 12 50013 000500 12 94013 00060 12 05112 00051 "Moved by" is the distance to the nearest round number. The biggest move is always close to halfway: 12 500 moves a full 500. The smallest move is a number that was almost round already: 12 051 moves 51. Work out each move; do not guess from the size of the number.
Estimate first, then trust or doubt your answer 38 217 + 24 906 = ? estimate 38 000 + 25 000 ≈ 63 000 exact 38 217 + 24 906 = 63 123 63 123 is close to 63 000 — believe it. An answer of 53 123 would be a signal to look again. The estimate is a check on the exact answer. It is never the answer.
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