Understand Powers of 10 Patterns - 5th Grade Math

1. What is the value of $10^1$?

   $10$. Ten to the first power is ten itself.

2. What is the value of $10^4$?

   $10000$. Ten to the fourth is 10,000.

3. What is the rule for multiplying a decimal by $10^n$?

   Multiply by $10^n$: move the decimal point $n$ places right. Each power of $10$ shifts digits left by that many places.

4. What is $0.006\times 10^2$?

   $0.6$. Move decimal 2 places right.

5. What is the value of $10^3$?

   $1000$. Ten cubed means $10 \times 10 \times 10$.

6. What is $0.56 \times 10^3$?

   $560$. Move decimal 3 places right: $0.56 \rightarrow 560$.

7. What is $3.7 \times 10^2$?

   $370$. Move decimal 2 places right: $3.7 \rightarrow 370$.

8. What is $8.4\times 10^2$?

   $840$. Move decimal 2 places right: $8.4 → 840$.

9. What is the value of $10^0$?

   $1$. Any number to the zero power equals one.

10. What is $47\times 10^3$?

    $47000$. Append 3 zeros to $47$ to get $47000$.

11. What is $0.49\times 10^3$?

    $490$. Move decimal 3 places right.

12. Identify the equivalent expression: $10^2 \times 10^3 = 10^{\square}$

    $10^5$. When multiplying powers, add exponents: $2 + 3 = 5$.

13. What is $6\times 10^0$?

    $6$. Multiplying by $10^0$ (which is 1) doesn't change the value.

14. What is $600 \times 10^2$?

    $60000$. $10^2 = 100$, so add 2 zeros to 600.

15. What is $0.56\times 10^3$?

    $560$. Move decimal 3 places right: $0.56 → 560$.

16. What is the rule for dividing a decimal by $10^n$?

    Divide by $10^n$: move the decimal point $n$ places left. Division shifts digits right, making the number smaller.

17. What is the pattern in the number of zeros in $10^n$?

    $10^n$ has exactly $n$ zeros for $n\ge 1$. The exponent equals the zero count (except $10^0=1$).

18. What is the value of $10^2$?

    $100$. Ten squared means $10 \times 10$.

19. What is $52.08\times 10^1$?

    $520.8$. Move decimal 1 place right.

20. What is $9 \times 10^4$?

    $90000$. $10^4 = 10000$, so add 4 zeros to 9.

21. What is $7.2\div 10^2$?

    $0.072$. Move decimal 2 places left.

22. What is $5.2\div 10^1$?

    $0.52$. Move decimal 1 place left: $5.2 → 0.52$.

23. What is $600\times 10^2$?

    $60000$. Append 2 zeros to $600$ to get $60000$.

24. What pattern describes $10^n$ written as a whole number for $n\ge 1$?

    $1$ followed by $n$ zeros. Each power of 10 adds another zero.

25. What is $4.005\times 10^2$?

    $400.5$. Move decimal 2 places right: $4.005 → 400.5$.

26. What is $12.04 \times 10^1$?

    $120.4$. Move decimal 1 place right: $12.04 \rightarrow 120.4$.

27. What happens to a whole number when it is multiplied by $10^n$?

    Append $n$ zeros to the right of the whole number. Multiplying by $10^n$ adds $n$ zeros to the end.

28. Find and correct the error: $4.2\times 10^2=4.200$.

    Correct: $4.2\times 10^2=420$. Decimal moves 2 places right, not adds zeros after decimal.

29. What is $3.07\times 10^1$?

    $30.7$. Move decimal 1 place right: $3.07 → 30.7$.

30. What is $7.2 \div 10^3$?

    $0.0072$. Move decimal 3 places left: $7.2 \rightarrow 0.0072$.

31. What is $67\div 10^2$?

    $0.67$. Move decimal 2 places left: $67 → 0.67$.

32. What is the rule for multiplying a whole number by $10^n$?

    Multiply by $10^n$: append $n$ zeros to the whole number. Each power of $10$ adds that many zeros to the end.

33. What is $480\div 10^2$?

    $4.8$. Move decimal 2 places left.

34. What is the value of $10^5 \div 10^2$?

    $10^3$. When dividing powers, subtract exponents: $5 - 2 = 3$.

35. What are the values of $10^0$, $10^1$, $10^2$, and $10^3$?

    $10^0=1$, $10^1=10$, $10^2=100$, $10^3=1000$. Each power of $10$ adds one more zero to the previous value.

36. Which expression is equal to $3.6\times 1000$: $3.6\times 10^3$ or $3.6\times 10^2$?

    $3.6\times 10^3$. $1000 = 10^3$, so use the first expression.

37. What is $48.6 \div 10^1$?

    $4.86$. Move decimal 1 place left: $48.6 \rightarrow 4.86$.

38. What is $0.5\div 10^3$?

    $0.0005$. Move decimal 3 places left.

39. What happens to the decimal point when a decimal is multiplied by $10^n$?

    Move the decimal point $n$ places to the right. Each power of 10 shifts the decimal one place right.

40. What is $12.3\div 10^1$?

    $1.23$. Move decimal 1 place left.

41. What happens to the decimal point when a decimal is divided by $10^n$?

    Move the decimal point $n$ places to the left. Each power of 10 shifts the decimal one place left.

42. What does $10^n$ mean when $n$ is a whole number?

    $10^n$ means $10$ multiplied by itself $n$ times. The exponent shows how many times to use $10$ as a factor.

43. What is $0.9\div 10^3$?

    $0.0009$. Move decimal 3 places left: $0.9 → 0.0009$.

44. What is $47 \times 10^3$?

    $47000$. $10^3 = 1000$, so add 3 zeros to 47.

45. What is $900\times 10^2$?

    $90000$. Append 2 zeros to 900.

46. What does the exponent mean in $10^n$ when $n$ is a whole number?

    $10^n$ is $1$ followed by $n$ zeros. The exponent tells you how many zeros follow the 1.

47. What is $1200\div 10^2$?

    $12$. Remove 2 zeros from $1200$ to get $12$.

48. What is $3.6\times 10^2$?

    $360$. Move decimal 2 places right.

49. What is $0.905 \div 10^2$?

    $0.00905$. Move decimal 2 places left: $0.905 \rightarrow 0.00905$.

50. What exponent $n$ makes $10^n=100000$?

    $n=5$. Count the zeros: $100000$ has 5 zeros.

51. What is the value of $10^0\times 7.3$?

    $7.3$. Since $10^0 = 1$, this equals $1 \times 7.3 = 7.3$.

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