Place value to 10 000 and Roman numerals – Year 4 maths worksheet answers to download as PDF

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1. Answer to Question 1

   1. 4 632 (4 thousands, 6 hundreds, 3 tens, 2 ones).
   2. 7 090: 7 thousands, no hundreds, 9 tens, no ones.
   3. Five thousand, three hundred and eight: there are no tens.
   4. Nine thousand and forty: 9 thousands, 0 hundreds, 4 tens, 0 ones.

2. Answer to Question 2

   Number	Th	H	T	O	Value of the digit
   6 285	6	2	8	5	200
   4 730	4	7	3	0	30
   8 106	8	1	0	6	8000
   2 599	2	5	9	9	9

   Each value is the digit times the value of its column: 2 × 100 = 200, 3 × 10 = 30, 8 × 1000 = 8000 and 9 × 1 = 9.

3. Answer to Question 3

   1. 3000 + 800 + 20 + 1.
   2. 5000 + 0 + 70 + 0, which is 5000 + 70.
   3. 9000 + 0 + 0 + 9, which is 9000 + 9.
   4. 6000 + 300 + 40 + 7 = 6 347.

4. Answer to Question 4

   1. 2 851 has the fewest thousands. For the three 5s compare hundreds: 5 218, 5 281, 5 812. Order: 2 851, 5 218, 5 281, 5 812.
   2. Compare hundreds: 7 900 first; then 7 090 and 7 099 have 0 hundreds; 7 009 has 0 tens. Order: 7 900, 7 099, 7 090, 7 009.
   3. 6 482 > 6 428 (8 tens is more than 2 tens) and 3 099 < 3 101 (0 hundreds is less than 1 hundred).

5. Answer to Question 5

   1. Add 1000 each time: 5 340, 6 340, 7 340.
   2. Subtract 100 each time: 9 300, 9 200, 9 100.
   3. Add 7 each time: 28 + 7 = 35, 35 + 7 = 42, 42 + 7 = 49. The next three numbers are 35, 42, 49.
   4. Add 25 each time: 100, 125, 150.

6. Answer to Question 6

   Number	Nearest 10	Nearest 100	Nearest 1000
   3 674	3 670	3 700	4 000
   5 249	5 250	5 200	5 000
   8 995	9 000	9 000	9 000

   For 5 249: the ones digit is 9 so round the tens up to 5 250. The tens digit is 4 so we round the hundreds down. For 8 995 we round up every time because of the 9 and the 5.

7. Answer to Question 7

   1. Both numbers have 4 thousands and 6 hundreds. Compare tens: Saturday has 3 tens and Sunday has 7 tens. So Sunday (4 673) had more fans.
   2. 4 637: the tens digit is 3, so round down to 4 600.
   3. 4 673: the ones digit is 3, so round down to 4 670.
   4. 7 500 − 4 637 = 2 863. To the nearest 100 this is 2 900 fans.

8. Answer to Question 8

   1. Fiction 3 258 rounds to 3 300. Non-fiction 1 940 rounds to 1 900. Picture books 2 062 rounds to 2 100.
   2. 3 258 → 3 000. 1 940 → 2 000. 2 062 → 2 000.
   3. Fiction has the most (3 258) and non-fiction has the fewest (1 940).
   4. He is right. 1 940 rounds up to 2 000 and 2 062 rounds down to 2 000. But the real numbers are not the same: they are only equal after rounding.

9. Answer to Question 9

   1. 2 035 has 0 hundreds, so it is smallest. 2 305 and 2 350 both have 3 hundreds, and 350 is bigger than 305. Order: 2 035, 2 305, 2 350.
   2. Zara has the most. 2 350 − 2 305 = 45 pennies more than Sam.
   3. 2 350 + 300 = 2 650 pennies (3 × 100 = 300).
   4. 2 305 + 50 = 2 355 pennies (5 × 10 = 50).

10. Answer to Question 10

    1. IX = 10 − 1 = 9 and XI = 10 + 1 = 11. XI is bigger.
    2. 4 = IV, 7 = V + II = VII, 12 = X + II = XII.
    3. XLVII = XL + VII = 40 + 7 = 47.
    4. 25 = XX + V = XXV; 75 = L + XX + V = LXXV.

11. Answer to Question 11

    1. 25, 50, 75, 100, 125, 150, 175, 200.
    2. The sixth number is 150 biscuits.
    3. 4 boxes make 100, so 400 = 4 × 100 = 16 boxes. Check: 16 × 25 = 400. 16 boxes.
    4. 1 000 ÷ 25 = 40 (four boxes make 100, and 10 × 4 = 40). 40 boxes.

12. Answer to Question 12

    1. Ben Nevis (1 345 m) is the highest and Helvellyn (950 m) the lowest.
    2. 1 345, 1 085, 978, 950.
    3. 1 345 → 1 300; 1 085 → 1 100; 978 → 1 000; 950 → 1 000.
    4. Scafell Pike and Helvellyn both round to 1 000 m.

13. Answer to Question 13

    1. Ones = 3, so thousands = 6. The number is 6 503.
    2. Six thousand, five hundred and three.
    3. The tens digit is 0, so we round down: 6 500.
    4. 6 503 + 1000 = 7 503; 6 503 − 100 = 6 403.

14. Answer to Question 14

    1. Sunday (3 150) is the most and Monday (1 096) the fewest.
    2. 1 296 → 1 300; 2 408 → 2 400; 3 150 → 3 200; 1 096 → 1 100.
    3. 1 300 + 2 400 + 3 200 + 1 100 = 8 000.
    4. The estimate is exactly 8 000, so the school was very close to the target.
    5. Friday: 1 296 → 1 000. Monday: 1 096 → 1 000. They agree: both round to 1 000, but 1 296 is about 200 bigger.

15. Answer to Question 15

    1. Put the biggest digit first, then the next biggest: 8 530.
    2. The smallest digit that is not zero goes first, then 0, then 5, then 8: 3 058.
    3. The number must start with 8 and end in an even digit. The only even digit left is 0, so the last digit is 0. The other two digits are 3 and 5 in either order: 8 350 and 8 530. There are 2 answers.
    4. 8 530 → 9 000. 3 058 → 3 000. 9 000 − 3 000 = 6 000.

16. Answer to Question 16

    Building	Roman label	Number
    Bridge arch	XCIV	94
    Castle wall	LXXXVIII	88
    Church bell	XLIX	49
    Lighthouse	CVII	107

    1. XCIV = 90 + 4 = 94; LXXXVIII = 50 + 30 + 8 = 88; XLIX = 40 + 9 = 49; CVII = 100 + 7 = 107.
    2. The oldest is the lighthouse (107); the youngest is the church bell (49).
    3. 49, 88, 94, 107.
    4. A letter I can only be taken away from V and X, not from C. 99 = 90 + 9 = XC + IX = XCIX.

17. Answer to Question 17

    1. Compare hundreds first: Bexley 7, Ashby 7, Dunmore 6, Corfe 0. Between Bexley (2 760) and Ashby (2 706), 6 tens beats 0 tens. Order: Bexley, Ashby, Dunmore, Corfe.
    2. 2 706 → 2 700; 2 760 → 2 800; 2 076 → 2 100; 2 670 → 2 700.
    3. 2 700 + 2 800 + 2 100 + 2 700 = 10 300. This is more than 10 000.
    4. 2 706 + 2 760 + 2 076 + 2 670 = 10 212, which is more than 10 000, so the lorry does not have enough space. Here the estimate gave the right answer, but if the exact total were 9 990 the estimate would be wrong, so we check with exact numbers.

18. Answer to Question 18

    1. LIV = 50 + 4 = 54; XLVI = 40 + 6 = 46; LXIII = 50 + 10 + 3 = 63; XCV = 90 + 5 = 95.
    2. XLVI (46), LIV (54), LXIII (63), XCV (95).
    3. 14 = X + IV = XIV; 29 = XX + IX = XXIX; 83 = L + XXX + III = LXXXIII.
    4. The Romans took away only one smaller letter, and I can only be taken away from V and X, never twice. 8 = 5 + 3, so it is VIII.

19. Answer to Question 19

    1. 4C has only 8 thousands, so it walked the least. The other three all have 9 thousands, so compare hundreds: 4D has 8, 4A has 4 and 4B has 0. Order: 4D, 4A, 4B, 4C.
    2. 9 480 → 9 500; 9 048 → 9 000; 8 940 → 8 900; 9 804 → 9 800.
    3. 9 500 + 9 000 + 8 900 + 9 800 = 37 200, which is less than 40 000. Exact total: 9 480 + 9 048 + 8 940 + 9 804 = 37 272. They did not reach the target; they were 2 728 steps short.
    4. 9 048 − 8 940 = 108 steps. That is about 100 steps, which is small compared with nine thousand, so she is roughly right.

20. Answer to Question 20

    1. A number rounds to 5 900 if it is from 5 850 up to 5 949, so the smallest is 5 850 and the largest is 5 949.
    2. The thousands digit is 5. The ones digit is double the tens digit and it must be a single digit, so the tens digit is 0, 1, 2, 3 or 4. That means the hundreds digit cannot be 8 (the tens digit would have to be 5 or more), so it is 9. List the numbers: 5 900, 5 912, 5 924, 5 936, 5 948. Digit sums: 14, 17, 20, 23 and 26. Only 5 936 has digit sum 23 and four different digits (5 900 repeats digits). Zara’s number is 5 936.