➕ Maths: Whole Numbers and the Number System

1. In the number 482,673, which digit is in the ten thousands place?

1. 4
2. 8
3. 2
4. 6

Reading from the right, the places are units, tens, hundreds, thousands, ten thousands, so the ten thousands digit in 482,673 is 8. (DfE, Functional Skills subject content: mathematics (February 2018), Level 2, 'Using numbers and the number system')

2. How is the number 'three hundred and six thousand, four hundred and twenty' written in figures?

1. 306,420
2. 360,420
3. 3,006,420
4. 306,042

Three hundred and six thousand is 306,000 and four hundred and twenty is 420, giving 306,420. (DfE, Functional Skills subject content: mathematics (February 2018), Level 1, 'Using numbers and the number system' (ref L1.1))

3. What is the value of the digit 7 in the number 752,914?

1. 7
2. 7,000
3. 70,000
4. 700,000

The 7 sits in the hundred thousands position, so its value is 700,000. (DfE, Functional Skills subject content: mathematics (February 2018), Level 2, 'Using numbers and the number system')

4. A council records its population as 1,000,000. How is this number read in words?

1. One hundred thousand
2. Ten million
3. One million
4. One billion

The number 1,000,000 is one followed by six zeros, which is read as one million. (DfE, Functional Skills subject content: mathematics (February 2018), Level 1, 'Using numbers and the number system' (ref L1.1))

5. Four towns report their populations as 89,400, 98,040, 89,040 and 90,400. Which town has the largest population?

1. 89,400
2. 98,040
3. 89,040
4. 90,400

Comparing from the highest place value, 98,040 has 9 in the ten thousands and the largest remaining digits, making it the greatest. (DfE, Functional Skills subject content: mathematics (February 2018), Level 2, 'Using numbers and the number system' (ref L2.1))

6. Which list of numbers is correctly ordered from smallest to largest?

1. 407,000; 470,000; 47,000; 740,000
2. 47,000; 407,000; 470,000; 740,000
3. 740,000; 470,000; 407,000; 47,000
4. 47,000; 470,000; 407,000; 740,000

Ordered by size the sequence is 47,000 then 407,000 then 470,000 then 740,000. (DfE, Functional Skills subject content: mathematics (February 2018), Level 2, 'Using numbers and the number system' (ref L2.1))

7. A digital display shows 250,000. What do the digits '0' to the right of the 25 represent in this number?

1. The number has been rounded
2. The thousands, hundreds, tens and units places are all empty
3. The number is negative
4. The number is less than 25

The zeros are place holders showing that the thousands, hundreds, tens and units positions contain no value, so the number is exactly 250,000. (Base-ten place value system; DfE, Functional Skills subject content: mathematics (February 2018), Level 2)

8. Each place value position in a whole number is how many times larger than the position immediately to its right?

1. 2 times larger
2. 5 times larger
3. 10 times larger
4. 100 times larger

In the base-ten system each place to the left is worth ten times the place immediately to its right. (Base-ten place value system; DfE, Functional Skills subject content: mathematics (February 2018), Level 1 (ref L1.1))

9. A factory made 6,500 items each day for 100 days. Using place value, how many items did it make in total?

1. 65,000
2. 650,000
3. 6,500,000
4. 6,050,000

Multiplying by 100 shifts every digit two places to the left, so 6,500 x 100 = 650,000. (DfE, Functional Skills subject content: mathematics (February 2018), Level 1, 'Using numbers and the number system' (ref L1.3))

10. In the number 538,162, the 5 and the 3 are swapped to make a new number. By how much does the value of the number change?

1. It increases by 200,000
2. It decreases by 200,000
3. It increases by 20,000
4. It does not change

538,162 becomes 358,162; the 5 (worth 500,000) and 3 (worth 300,000) trade places, reducing the total by 200,000. (Base-ten place value system; DfE, Functional Skills subject content: mathematics (February 2018), Level 2 (ref L2.1))

11. When rounding, what should you do if the digit immediately to the right of the rounding place is 5, 6, 7, 8 or 9?

1. Leave the rounding digit unchanged
2. Increase the rounding digit by 1
3. Decrease the rounding digit by 1
4. Delete the rounding digit

Under round-half-up rules, a digit of 5 to 9 means you round up, increasing the rounding digit by 1. (Standard rounding (round-half-up) rules; aligned to DfE L1.12 and L2.2)

12. What is 7.83 rounded to one decimal place?

1. 7.8
2. 7.9
3. 8.0
4. 7.83

The second decimal digit is 3, which is 0 to 4, so the first decimal digit stays as 8, giving 7.8. (DfE, Functional Skills subject content: mathematics (February 2018), Level 1, 'Using numbers and the number system' (ref L1.12))

13. What is 12.467 rounded to two decimal places?

1. 12.46
2. 12.47
3. 12.50
4. 12.4

The third decimal digit is 7, so the second decimal digit rounds up from 6 to 7, giving 12.47. (DfE, Functional Skills subject content: mathematics (February 2018), Level 1, 'Using numbers and the number system' (ref L1.12))

14. What is 9.95 rounded to one decimal place?

1. 9.9
2. 9.95
3. 10.0
4. 9.5

The second decimal digit is 5, so 9.9 rounds up to 10.0. (DfE, Functional Skills subject content: mathematics (February 2018), Level 1, 'Using numbers and the number system' (ref L1.12))

15. What is the first significant figure in the number 0.00472?

1. 0
2. 4
3. 7
4. 2

Leading zeros are not significant; the first significant figure is the first non-zero digit, which is 4. (Standard significant-figures convention; aligned to DfE L2.2 'estimation, approximation')

16. What is 6,482 rounded to one significant figure?

1. 6,000
2. 6,500
3. 7,000
4. 6,400

The first significant figure is 6 (thousands); the next digit is 4, so it rounds down, giving 6,000. (Standard significant-figures convention; aligned to DfE L2.2 'estimation, approximation')

17. What is 38,750 rounded to two significant figures?

1. 38,000
2. 39,000
3. 40,000
4. 38,800

The first two significant figures are 3 and 8; the next digit is 7, so 38 rounds up to 39, giving 39,000. (Standard significant-figures convention; aligned to DfE L2.2 'estimation, approximation')

18. A shop's annual takings were 247,830 pounds. What is this rounded to the nearest ten thousand pounds?

1. 240,000 pounds
2. 248,000 pounds
3. 250,000 pounds
4. 200,000 pounds

The thousands digit is 7, which is 5 or more, so the ten thousands digit rounds up from 4 to 5, giving 250,000. (Standard rounding (round-half-up) rules; aligned to DfE L2.2)

19. To estimate 312 x 49, you round each number to one significant figure. Which calculation should you carry out?

1. 310 x 50
2. 300 x 50
3. 300 x 40
4. 320 x 50

Rounded to one significant figure, 312 becomes 300 and 49 becomes 50, so the estimate is 300 x 50 = 15,000. (Standard estimation method using rounding to 1 significant figure; aligned to DfE L2.2 'estimation, approximation')

20. A learner uses estimation to check 6,043 + 3,920. Which rounded calculation gives a sensible estimate?

1. 6,000 + 4,000 = 10,000
2. 6,000 + 3,000 = 9,000
3. 7,000 + 4,000 = 11,000
4. 6,100 + 3,900 = 10,000

Rounding each value to one significant figure gives 6,000 and 4,000, so the estimate is 10,000, close to the exact answer of 9,963. (Standard estimation method; aligned to DfE L2.2 'using strategies to check answers including estimation and approximation')

21. What is 0.0396 rounded to two significant figures?

1. 0.04
2. 0.039
3. 0.040
4. 0.0396

The first two significant figures are 3 and 9; the next digit is 6, so 39 rounds up to 40, giving 0.040. (Standard significant-figures convention; aligned to DfE L2.2 'estimation, approximation')

22. What is 199.96 rounded to one decimal place?

1. 199.9
2. 199.96
3. 200.0
4. 200.1

The second decimal digit is 6, so 199.9 rounds up; carrying through gives 200.0. (DfE, Functional Skills subject content: mathematics (February 2018), Level 1, 'Using numbers and the number system' (ref L1.12))

23. A calculator gives 47,182 ÷ 61 = 773.47... A learner rounds 47,182 to 47,000 and 61 to 60 to estimate the answer. What is the best reason this estimate is useful?

1. It gives the exact answer more quickly
2. It gives a rough value (about 780) to check the calculation is reasonable
3. It removes the need to use a calculator at all
4. It always gives a larger answer than the true value

Estimating with rounded numbers gives roughly 47,000 ÷ 60 ≈ 783, a quick check that the calculator answer of about 773 is sensible. (DfE, Functional Skills subject content: mathematics (February 2018), Level 2, 'Using numbers and the number system' (ref L2.2))

24. A stadium can hold ninety thousand and nine spectators. How is this written in figures?

1. 9,009
2. 90,009
3. 90,900
4. 900,009

Ninety thousand is 90,000 and nine units is 9, with zeros holding the hundreds and tens places, giving 90,009. (DfE, Functional Skills subject content: mathematics (February 2018), Level 1, 'Using numbers and the number system' (ref L1.1))

25. What is the result of 4,287 + 1,956?

1. 6,243
2. 6,143
3. 6,233
4. 5,243

Adding the two whole numbers column by column gives 4,287 + 1,956 = 6,243. (DfE, Functional Skills subject content: mathematics (February 2018), Level 2, 'Using numbers and the number system' (ref L2.2))

26. What is 9,000 - 3,475?

1. 5,525
2. 5,625
3. 6,525
4. 5,535

Subtracting gives 9,000 - 3,475 = 5,525. (DfE, Functional Skills subject content: mathematics (February 2018), Level 2, 'Using numbers and the number system' (ref L2.2))

27. What is 36 multiplied by 25?

1. 900
2. 850
3. 950
4. 800

36 x 25 = 900 (for example, 36 x 100 = 3,600, then divide by 4). (DfE, Functional Skills subject content: mathematics (February 2018), Level 2, 'Using numbers and the number system' (ref L2.2))

28. What is 4,896 divided by 8?

1. 612
2. 622
3. 618
4. 602

4,896 ÷ 8 = 612 with no remainder. (DfE, Functional Skills subject content: mathematics (February 2018), Level 2, 'Using numbers and the number system' (ref L2.2))

29. A warehouse holds 245,600 items. A delivery adds 78,950 more. How many items are there in total?

1. 324,550
2. 323,550
3. 324,650
4. 314,550

245,600 + 78,950 = 324,550 items, a calculation with numbers up to one million as required at Level 2. (DfE, Functional Skills subject content: mathematics (February 2018), Level 2, 'Using numbers and the number system' (ref L2.2))

30. A delivery van travels 384 miles each day for 6 days. How many miles does it travel in total?

1. 2,304
2. 2,294
3. 2,404
4. 2,104

384 x 6 = 2,304 miles in total. (DfE, Functional Skills subject content: mathematics (February 2018), Level 2, 'Using numbers and the number system' (ref L2.2))

31. A charity collects £15,372 and shares it equally between 12 local projects. How much does each project receive?

1. £1,281
2. £1,271
3. £1,381
4. £1,261

15,372 ÷ 12 = 1,281, so each project receives £1,281. (DfE, Functional Skills subject content: mathematics (February 2018), Level 2, 'Using numbers and the number system' (ref L2.2))

32. A town's population was 128,450. Over a year 6,380 people left and 9,215 moved in. What is the new population?

1. 131,285
2. 131,185
3. 125,615
4. 131,385

128,450 - 6,380 + 9,215 = 131,285 people. (DfE, Functional Skills subject content: mathematics (February 2018), Level 2, 'Using numbers and the number system' (ref L2.2))

33. A box holds 144 screws. A factory needs 5,000 screws. How many full boxes are required to provide at least 5,000 screws?

1. 35
2. 34
3. 36
4. 37

5,000 ÷ 144 = 34.7..., so 35 full boxes (giving 5,040 screws) are needed to reach at least 5,000. (DfE, Functional Skills subject content: mathematics (February 2018), Level 2, 'Using numbers and the number system' (ref L2.2))

34. A company orders 1,250 laptops at £478 each. What is the total cost?

1. £597,500
2. £587,500
3. £597,050
4. £598,500

1,250 x 478 = 597,500, so the total cost is £597,500. (DfE, Functional Skills subject content: mathematics (February 2018), Level 2, 'Using numbers and the number system' (ref L2.2))

35. The temperature falls from 4 degrees Celsius to -7 degrees Celsius overnight. By how many degrees did the temperature fall?

1. 11 degrees
2. 3 degrees
3. 7 degrees
4. 9 degrees

The change is 4 - (-7) = 4 + 7 = 11 degrees, because subtracting a negative is the same as adding its positive value. (Standard integer arithmetic rules for addition and subtraction of negative numbers (GCSE/Functional Skills number content))