Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
15 questions · official format, shuffled order
1 The number 6 349 702 is rounded to the nearest million, and the same number is rounded to the nearest ten thousand. What is the difference between the two answers?
Show worked solution
Nearest million: the hundred-thousands digit is 3, so 6 000 000. Nearest ten thousand: the thousands digit is 9, so 6 340 000 rounds up to 6 350 000. The difference is 6 350 000 − 6 000 000 = 350 000.
2 In the number 70 020, the value of the 7 is how many times the value of the 2?
Show worked solution
The 7 is worth 70 000 and the 2 is worth 20. 70 000 ÷ 20 = 3 500. Dividing the digits themselves (7 ÷ 2) ignores where they sit.
3 At 6 pm the temperature is −3 °C. It falls 2 °C every hour until midnight, then rises 1 °C every hour. What is the temperature at 4 am?
Show worked solution
6 pm to midnight is 6 hours: −3 − 12 = −15 °C. Midnight to 4 am is 4 hours: −15 + 4 = −11 °C.
4 Use each of these digit cards once to make the largest even five-digit number, and once more to make the smallest five-digit number. What is the difference between the two numbers?
Show worked solution
Largest even number: 97 420 (its last digit 0 is even). Smallest number: 20 479, because 0 cannot go first. 97 420 − 20 479 = 76 941.
5 P and Q are marked on this number line. What is the difference between the two numbers?
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P is −15 and Q is 10. From −15 to 0 is 15, and from 0 to 10 is 10, so the difference is 25.
6 Look at the number 3 406 950.1 Rounded to the nearest hundred thousand it is 3 400 000.
2 The digit 6 is worth 60 000.
3 It is between 3.4 million and 3.5 million.
Which statements are correct?
2 The digit 6 is worth 60 000.
3 It is between 3.4 million and 3.5 million.
Which statements are correct?
Show worked solution
The ten-thousands digit is 0, so it rounds down to 3 400 000 (1 ✓). The 6 is in the thousands column, worth 6 000, not 60 000 (2 ✗). 3 406 950 lies between 3 400 000 and 3 500 000 (3 ✓). 1 and 3.
7 A charity raised three million dollars. Every donation was exactly $250. How many donations were there?
Show worked solution
Four 250s make 1 000, so 3 000 000 ÷ 250 = 3 000 × 4 = 12 000 donations.
8 What is 40 000 more than 2 968 300, rounded to the nearest hundred thousand?
Show worked solution
2 968 300 + 40 000 = 3 008 300. To the nearest hundred thousand, the ten-thousands digit is 0, so it rounds down to 3 000 000.
9 A diver is at −18 m. A fish is 7 m below her, and a boat is 23 m directly above the fish. At what height is the boat?
Show worked solution
The fish is at −18 − 7 = −25 m. The boat is 23 m above that: −25 + 23 = −2 m, still 2 m below the surface.
10 The table shows the populations of five towns. Which town has the second largest population?
Show worked solution
The three numbers starting 2 1.. beat the two starting 2 0... Among them Bray is 2 100 001, Dunn is 2 100 000 and Ashby is 2 099 999, so the second largest is Dunn.
11 A number rounded to the nearest thousand is 48 000. Which of these could the number be?
Show worked solution
Everything from 47 500 up to 48 499 rounds to 48 000. 47 499 rounds to 47 000; 48 500 and 48 501 round to 49 000. Only 47 500 works.
12 In a five-digit number, the digit 8 is worth 1 600 times the digit 5. Which of these could be the number?
Show worked solution
The 8 must be worth 8 000 (thousands) and the 5 must be worth 5 (ones). In 78 015 the 8 is in the thousands and the 5 is in the ones. In 18 050 the 5 is worth 50; in 60 805 the 8 is worth 800.
13 Two arrows are marked on this number line.1 The difference between L and R is 11.
2 The number halfway between L and R is −3.
3 Adding 7 to L gives 0.
Which statements are correct?
2 The number halfway between L and R is −3.
3 Adding 7 to L gives 0.
Which statements are correct?
Show worked solution
L is −7 and R is 4. The difference is 7 + 4 = 11 (1 ✓). Halfway is 5.5 along from −7, which is −1.5, not −3 (2 ✗). −7 + 7 = 0 (3 ✓). 1 and 3.
14 What is the difference between the largest five-digit number with all its digits different and the smallest four-digit number with all its digits different?
Show worked solution
Largest with different digits: 98 765. Smallest four-digit with different digits: 1 023 (not 1 000, which repeats 0). 98 765 − 1 023 = 97 742.
15 A number starts at 175 000 and is doubled again and again. How many doublings are needed before it is more than 3 million?
Show worked solution
175 000 → 350 000 → 700 000 → 1 400 000 → 2 800 000 → 5 600 000. After 4 doublings it is 2 800 000, still under 3 million; the 5th doubling takes it past.