Place value & directed numbers

Every digit in a number has a value based on its position — in 4,285 the 4 means 4,000, not just "4". Directed numbers are positive and negative numbers, used for things like temperature or being in debt. A negative number sits below zero on a number line — the further left, the smaller the number, so −5 is less than −2.

Key terms

Place value:

The value of a digit based on its position in a number.

Directed number:

A positive or negative number, showing direction from zero.

Number line:

A line showing numbers in order, with negatives to the left of zero.

Questions

1. 1. In 4,285, what does the 4 represent?

   • 4
   • 40
   • 400
   • 4,000

2. 2. In 573, what does the 7 represent?

   • 7
   • 70
   • 700
   • 7,000

3. 3. Which is colder, −5°C or −2°C?

   • −5°C
   • −2°C
   • Same
   • Cannot tell

4. 4. A negative number is:

   • Above zero
   • Below zero
   • Always zero
   • Not a real number

5. 5. Which number is smallest?

   • −10
   • −2
   • 0
   • 5

6. 6. If your bank balance is −$20, you:

   • Have $20 saved
   • Owe $20
   • Have $0
   • Have $200

7. 7. In 9,142, what does the 9 represent?

   • 9
   • 90
   • 900
   • 9,000

8. 8. Order from smallest to largest: −3, 2, −1, 0

   • −3, −1, 0, 2
   • 2, 0, −1, −3
   • 0, −1, −3, 2
   • −1, −3, 0, 2

9. 9. The temperature rises from −4°C by 6 degrees. What is the new temperature?

   • −10°C
   • −2°C
   • 2°C
   • 10°C

10. 10. Which is greater, −8 or −3?

    • −8
    • −3
    • Equal
    • Cannot tell

11. 11. A lift goes from level 2 down 5 levels. What level is it now?

    • −3
    • 3
    • 7
    • −5

12. 12. In 60,347, what does the 6 represent?

    • 6
    • 600
    • 6,000
    • 60,000

13. 13. Your account has −$15. You deposit $10. What is the new balance?

    • −$25
    • −$5
    • $5
    • $25

14. 14. Which list is ordered from largest to smallest?

    • 5, 1, −2, −6
    • −6, −2, 1, 5
    • 1, 5, −2, −6
    • −2, −6, 1, 5

15. 15. The temperature is −6°C at 6am and rises steadily to 8°C by noon. How many degrees did it rise?

    • 2
    • 8
    • 14
    • 48

16. 16. A submarine is at −120m (below sea level) and rises 45m. What is its new depth?

    • −165m
    • −75m
    • 75m
    • 165m

17. 17. Your account is −$40. You need it to reach $0. How much must you deposit?

    • $0
    • $20
    • $40
    • −$40

18. 18. Which of these is equivalent to "500 thousand plus 6 hundred"?

    • 506
    • 5,600
    • 500,600
    • 56,000

19. 19. A city's temperature drops from 3°C by 9 degrees overnight. What is the new temperature?

    • −12°C
    • −6°C
    • 6°C
    • 12°C

20. 20. Which of these numbers has the digit 7 worth exactly 70,000?

    • 173,209
    • 705,209
    • 17,209
    • 507,209

21. 21. Two lifts start at level 0. One goes up 8, the other down 5. How many levels apart are they?

    • 3
    • 5
    • 8
    • 13