Multiple Choice

1. What is the standard form value of the expression $10^5$?

   100,000

   1,000

   50,000

   100,000,000

2. Simplify the expression $2^{-3}$.

   $-8$

   $\frac{1}{8}$

   6

   $-\frac{1}{8}$

3. What is the value of $10^{-4}$?

   $10,000$

   $0.0001$

   $0.001$

   $0.00001$

4. Use the product rule of exponents to simplify $5^2 \times 5^3$.

   $5^5$

   $25^5$

   $5^6$

5. In the scientific notation number $3.5 \times 10^7$, what is the name for the number $3.5$?

   The magnitude

   The power

   The exponent

   The coefficient (or mantissa)

6. For a number to be correctly written in scientific notation, the absolute value of the coefficient, $|a|$, must satisfy which condition?

   $0 < |a| \le 1$

   $1 < |a| < 10$

   $|a| \le 10$

   $1 \le |a| < 10$

7. Which of the following numbers is NOT correctly written in scientific notation?

   $5 \times 10^{12}$

   $1.002 \times 10^6$

   $9.99 \times 10^{-3}$

   $12.1 \times 10^5$

8. Convert the large number $4,500,000$ into scientific notation.

   $45 \times 10^5$

   $4.5 \times 10^7$

   $4.5 \times 10^6$

   $0.45 \times 10^7$

9. Convert $6.2 \times 10^8$ from scientific notation to standard form.

   $620,000,000,000$

   $6,200,000$

   $620,000,000$

   $62,000,000$

10. Express 980 billion in scientific notation.

    $0.98 \times 10^{12}$

    $9.8 \times 10^{10}$

    $9.8 \times 10^{12}$

    $9.8 \times 10^{11}$

11. Convert $1.003 \times 10^4$ to standard form.

    $10,030$

    $1,003,000$

    $100.3$

    $1,000,300$

12. Convert the small number $0.000071$ into scientific notation.

    $7.1 \times 10^{-5}$

    $7.1 \times 10^5$

    $0.71 \times 10^{-4}$

    $7.1 \times 10^{-6}$

13. Convert $2.5 \times 10^{-6}$ from scientific notation to standard form.

    $0.0000025$

    $2,500,000$

    $0.00025$

14. Write $0.001$ in scientific notation.

    $1 \times 10^{-3}$

    $10 \times 10^{-4}$

    $1 \times 10^3$

    $1 \times 10^{-2}$

15. Convert $9.9 \times 10^{-2}$ to standard form.

    $0.099$

    $0.99$

    $0.0099$

    $990$

16. Normalize the number $15 \times 10^5$.

    $1.5 \times 10^6$

    $15 \times 10^5$

    $0.15 \times 10^7$

    $1.5 \times 10^4$

17. Normalize $0.4 \times 10^{-3}$.

    $4 \times 10^{-3}$

    $40 \times 10^{-5}$

    $4 \times 10^{-4}$

    $4 \times 10^{-2}$

18. What is the normalized scientific notation form of $100 \times 10^2$?

    $100 \times 10^2$

    $1 \times 10^2$

    $10 \times 10^3$

    $1 \times 10^4$

19. Determine the order of magnitude for the number $5.9 \times 10^4$.

    $10^3$

    $10^5$

    $10^4$

    $10^6$

20. What is the order of magnitude for the number $3.1 \times 10^9$?

    $10^8$

    $10^9$

    $10^{10}$

    $3 \times 10^9$

21. Estimate the magnitude of $8,100,000$ to the nearest power of ten.

    $10^6$

    $8 \times 10^6$

    $10^7$

    $10^8$

22. What is the order of magnitude of $7.5 \times 10^{-5}$?

    $10^{-5}$

    $10^{-4}$

    $10^{-6}$

    $8 \times 10^{-5}$

23. Which number is larger: $A = 2.1 \times 10^5$ or $B = 9.8 \times 10^4$?

    They are equal.

    $2.1 \times 10^4$

    $A$ is larger because it has a greater exponent.

    $B$ is larger because 9.8 is larger than 2.1.

24. Which number is the smallest: $5.3 \times 10^{-7}$, $1.1 \times 10^{-7}$, or $9.0 \times 10^{-7}$?

    $5.3 \times 10^{-7}$

    They are all the same size.

    $1.1 \times 10^{-7}$

    $9.0 \times 10^{-7}$

25. Compare $P = 5.1 \times 10^3$ and $Q = 51 \times 10^2$.

    $Q > P$

    $P = Q$

    $P > Q$

    The comparison cannot be made until $Q$ is normalized.

26. Multiply $(2 \times 10^4)(3 \times 10^5)$. Express the result in scientific notation.

    $6 \times 10^{20}$

    $6 \times 10^1$

    $6 \times 10^9$

    $5 \times 10^9$

27. Calculate the product of $(5 \times 10^2)(6 \times 10^3)$ and express the result in scientific notation.

    $30 \times 10^5$

    $3.0 \times 10^6$

    $3.0 \times 10^5$

    $3.0 \times 10^7$

28. Find the product of $(1 \times 10^{-2})(9 \times 10^5)$.

    $9 \times 10^3$

    $9 \times 10^7$

    $9 \times 10^{-10}$

29. Evaluate $(4 \times 10^{-8})(2 \times 10^{-3})$.

    $8 \times 10^{-5}$

    $8 \times 10^{11}$

    $8 \times 10^{-11}$

    $8 \times 10^{24}$

30. Calculate $(1.2 \times 10^1) \times (3 \times 10^2)$.

    $3.6 \times 10^2$

    $36 \times 10^3$

    $3.6 \times 10^3$

31. Divide $(8 \times 10^6) / (2 \times 10^3)$.

    $4 \times 10^2$

    $4 \times 10^3$

    $4 \times 10^9$

    $16 \times 10^3$

32. Calculate the quotient of $(3 \times 10^5) / (6 \times 10^2)$ and ensure the answer is in scientific notation.

    $2 \times 10^3$

    $0.5 \times 10^3$

    $5 \times 10^2$

33. Evaluate $(9 \times 10^{-4}) / (3 \times 10^{-6})$.

    $3 \times 10^{-2}$

    $3 \times 10^{-1}$

    $3 \times 10^{-10}$

    $3 \times 10^2$

34. Divide $(4 \times 10^2) / (8 \times 10^5)$.

    $2 \times 10^{-3}$

    $5 \times 10^{-4}$

    $0.5 \times 10^{-3}$

    $5 \times 10^2$

35. Calculate $(2.4 \times 10^7) / (6 \times 10^4)$.

    $14.4 \times 10^{11}$

    $0.4 \times 10^3$

    $4 \times 10^3$

    $4 \times 10^2$

36. To add $3 \times 10^4$ and $2 \times 10^5$, how must $3 \times 10^4$ be rewritten to match the exponent $10^5$?

    $3 \times 10^{10}$

    $30 \times 10^5$

    $0.3 \times 10^5$

    $0.03 \times 10^5$

37. To subtract $8 \times 10^6 - 1 \times 10^5$, how should $1 \times 10^5$ be adjusted to match the exponent $10^6$?

    $0.01 \times 10^6$

    $1 \times 10^6$

    $10 \times 10^6$

    $0.1 \times 10^6$

38. Rewrite $7.5 \times 10^{-2}$ so that the power of ten is $10^{-3}$.

    $75 \times 10^{-3}$

    $7.5 \times 10^{-3}$

    $0.75 \times 10^{-3}$

39. Rewrite $1.1 \times 10^8$ so that the power of ten is $10^9$.

    $11 \times 10^9$

    $0.11 \times 10^8$

    $1.1 \times 10^9$

    $0.11 \times 10^9$

40. Which expression correctly shows the step needed to add $5 \times 10^3 + 60 \times 10^2$? (Hint: use $10^3$ as the common exponent)

    $(5 + 600) \times 10^3$

    $(5 + 0.6) \times 10^3$

    $(5 + 60) \times 10^3$

    $(5 + 6) \times 10^3$