Place value to 10 000 000 and rounding – Year 6 maths worksheet answers to download as PDF

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1. Answer to Question 1

   1. Four million, three hundred and five thousand and sixty-two.
   2. Eight million, seventy thousand, nine hundred.
   3. 6 208 009. There are no ten thousands, no hundreds and no tens, so each of those columns holds a zero.
   4. 7 000 040. Seven million and 4 tens, with zeros in every other column.

   Ten million has eight digits: a 1 followed by seven zeros, which is 10 000 000. Zara's number 1 000 000 is only one million, ten times too small.

2. Answer to Question 2

   1. The 6 is in the ten thousands column, so its value is 60 000.
   2. The 4 is in the hundred thousands column, so its value is 400 000.
   3. The digit 2.
   4. 3 000 000 + 400 000 + 60 000 + 2 000 + 800 + 10 + 0 = 3 462 810.
   5. The 8 is in the ten thousands column (7 | 4 | 8 | 0 | 0 | 1 | 3), so its value is 80 000.

3. Answer to Question 3

   1. All four have seven digits and start with 3. Compare the hundred thousands: 4, 4, 5, 4. So 3 540 020 is the biggest. For the other three compare the ten thousands: 5, 0, 5. So 3 405 200 is the smallest. Finally 3 450 020 and 3 450 200 differ in the hundreds: 0 and 2. The order is 3 405 200, 3 450 020, 3 450 200, 3 540 020.
   2. 8 120 456 > 8 102 999 because 12 ten thousands is more than 10 ten thousands. 5 099 999 < 5 100 000, so the signs are > and <.
   3. The differences from 3 500 000 are 94 800, 49 980, 49 800 and 40 020. The closest is 3 540 020.

4. Answer to Question 4

   1. The ones digit is 7, so round up: 48 640.
   2. Tens digit 3, round down: 48 600. Hundreds digit 6, round up: 49 000.
   3. The thousands digit is 4, so round down: 350 000. The ten thousands digit is 5, so round up: 400 000.
   4. The hundred thousands digit is 4, so round down: 6 000 000.
   5. The hundreds digit is 5, so round up. The 9s carry: 3 000 000.

5. Answer to Question 5

   1. 2 995 000 + 10 000 = 3 005 000 (the 9 carries into the hundred thousands).
   2. The hundred thousands column holds 0, so exchange from the millions: 4 050 000 − 100 000 = 3 950 000.
   3. 899 500 + 1 000 = 900 500.
   4. 10 000 000 − 1 000 000 = 9 000 000.
   5. The sequence goes up by 100 000 each time: 2 650 000, 2 750 000, 2 850 000.

6. Answer to Question 6

   1. −3 + 8 = 5°C (3 steps to reach 0, then 5 more).
   2. −10, −7, −2, 0, 4. The further left, the smaller.
   3. From −4 up to 0 is 4, then up to 6 is 6. The difference is 4 + 6 = 10.
   4. −12 + 5 = −7 m.
   5. −9°C is colder, because −9 is further left than −2.

7. Answer to Question 7

   1. Wembley (90 000), Old Trafford (74 310), Celtic Park (60 411), Villa Park (42 682).
   2. 90 000, 74 000, 60 000, 43 000.
   3. 90 000, 70 000, 60 000, 40 000.
   4. 90 000 − 42 682 = 47 318.
   5. 74 310 to the nearest 10 000 is 70 000, so yes.

8. Answer to Question 8

   1. Greatest: Leeds. Smallest: Cardiff.
   2. Leeds 800 000, Sheffield 600 000, Bristol 500 000, Cardiff 400 000.
   3. No two of them match, so no. Cardiff (362 000) rounds up to 400 000 and Bristol (472 400) rounds up to 500 000, so the four answers are all different.
   4. Nearest million: 9 000 000 (the hundred thousands digit is 8, so round up). Nearest 100 000: 8 900 000 (the ten thousands digit is 6, so round up).
   5. Each city has six digits. The London number has seven digits.

9. Answer to Question 9

   1. Ben Nevis −11, Aberdeen −7, Inverness −4, Belfast −1, Manchester 2, Cardiff 5.
   2. From −11 to 0 is 11, then to 5 is 5, so the difference is 16 degrees.
   3. 2 − 6 = −4°C.
   4. −1 − 3 = −4, so Inverness.
   5. −4 + 9 = 5, which is above freezing.

10. Answer to Question 10

    1. Anything from 46 500 upwards rounds up to 47 000, so the smallest is 46 500.
    2. The largest is 47 499, because 47 500 would round up to 48 000.
    3. No. The crowd was at most 47 499, which is less than 47 500, so the stadium could not have been full.
    4. Rounding to the nearest 100 narrows the range to between 46 950 and 47 049, which is a much smaller range than 46 500 to 47 499.

11. Answer to Question 11

    1. Three hundred and eighty-four thousand, four hundred. One million, three hundred and ninety-one thousand.
    2. Nearest 100 000: 1 400 000. Nearest million: 1 000 000.
    3. 380 000.
    4. 40 075, 139 820, 384 400, 1 391 000.
    5. 30 × 40 075 = 1 202 250, and 1 391 000 is more than that. Yes, Leo is correct. (1 391 000 ÷ 40 075 is about 34.7.)

12. Answer to Question 12

    1. Lowest: the submarine (−150 m). Highest: Ben Nevis (1 345 m).
    2. 1 345 + 2 = 1 347 m.
    3. −150 + 85 = −65 m, so 65 m below sea level.
    4. 0 − 35 + 12 = −23 m.
    5. 1 300 m.

13. Answer to Question 13

    1. Nearest 10 000: 3 480 000. Nearest 100 000: 3 500 000.
    2. 4 000 000 − 3 482 719 = 517 281 copies.
    3. 3 000 000 × 4 = about £12 000 000.
    4. 3 482 719 + 517 281 = 4 000 000 exactly. The company reaches its target.

14. Answer to Question 14

    1. Five hundred and twelve thousand, four hundred and eighty.
    2. 2022: 420 000, 2023: 490 000, 2024: 510 000.
    3. 2024: 512 480 − 415 230 = 97 250 more.
    4. 420 000 + 490 000 + 510 000 = 1 420 000.
    5. Exact total 415 230 + 487 900 + 512 480 = 1 415 610. Needed: 1 500 000 − 1 415 610 = 84 390 more.

15. Answer to Question 15

    1. Round 1: 1 200 000. Round 2: 2 400 000. Round 3: 2 000 000. Round 4: 800 000.
    2. 1 200 000 + 2 400 000 + 2 000 000 + 800 000 = 6 400 000.
    3. 1 234 560 + 2 408 330 = 3 642 890. Adding 1 950 760 gives 5 593 650. Adding 849 999 gives 6 443 649.
    4. 6 443 649 − 6 400 000 = 43 649.
    5. 7 000 000 − 6 443 649 = 556 351 tickets. To the nearest 10 000 this is 560 000.
    6. The first two rounds sold 3 642 890 tickets. Half of 7 000 000 is 3 500 000, and 3 642 890 is bigger, so the journalist is right.

16. Answer to Question 16

    1. Put the digits in descending order: 9 753 210. Nine million, seven hundred and fifty-three thousand, two hundred and ten.
    2. The smallest digit that is not 0 goes first: 1 023 579.
    3. 9 753 210 − 1 023 579 = 8 729 631.
    4. The ten thousands digit is 5, so round up: 9 800 000.
    5. For example 7 395 012 (7 is in the millions, 9 in the ten thousands). Many answers are possible, provided each digit is used once.

17. Answer to Question 17

    1. 7 000 000 − 6 540 000 = 460 000 books.
    2. 460 000 ÷ 46 000 = 10 weeks.
    3. The hundred thousands digit is 5, so it rounds up: 7 000 000.
    4. After 6 weeks: 6 540 000 + 6 × 46 000 = 6 540 000 + 276 000 = 6 816 000. This is less than 7 000 000, so the target is not reached.
    5. 10 000 000 − 6 540 000 = 3 460 000 books.

18. Answer to Question 18

    1. To round to 3 800 000 to the nearest 100 000, the number must be 3 750 000 or more. (3 749 999 would round down to 3 700 000.)
    2. To round to 3 750 000 to the nearest 10 000 the number must be less than 3 755 000. So the smallest is 3 750 000 and the largest is 3 754 999.
    3. The number must be at least 3 751 500, so the smallest is 3 751 500.
    4. 3 752 000 (or any number from 3 751 500 to 3 752 499) fits all three clues.

19. Answer to Question 19

    1. Coldest: Wednesday (−21°C). Warmest: Saturday (−4°C).
    2. From −12 to −21: 9 degrees.
    3. Wed to Thu: +6; Thu to Fri: +6; Fri to Sat: +5. The biggest rise is 6 degrees, which happened on both Wed to Thu and Thu to Fri.
    4. Mon, Tue, Wed and Thu: 4 days.
    5. −7 + 10 = 3°C.
    6. Range = highest − lowest = −4 − (−21) = 17. She is correct.

20. Answer to Question 20

    1. Millions 3; hundred thousands 6; ten thousands 5; thousands 6 − 3 = 3; hundreds 0; tens 4 (the only square between 1 and 9 is 4); ones 2. The code is 3 653 042: three million, six hundred and fifty-three thousand and forty-two.
    2. Nearest 1 000: 3 653 000. Nearest 10 000: 3 650 000. Nearest 100 000: 3 700 000.
    3. 3 653 042 + 346 958 = 4 000 000. Check: 3 700 000 + 300 000 = 4 000 000. The estimate agrees.