Test Questions on Multiplying and Dividing Scientific Notation

📚 Quick Study Guide

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• Scientific Notation: A way to express very large or very small numbers as a number between 1 and 10 multiplied by a power of 10. The general form is $a \times 10^b$, where $1 \le |a| < 10$ and $b$ is an integer.
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• Multiplying Scientific Notation: Multiply the numbers ($a$ values) and add the exponents ($b$ values). $(a \times 10^b) \times (c \times 10^d) = (a \times c) \times 10^{(b+d)}$. Make sure the resulting $a$ value is between 1 and 10; adjust the exponent accordingly.
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• Dividing Scientific Notation: Divide the numbers ($a$ values) and subtract the exponents ($b$ values). $(a \times 10^b) / (c \times 10^d) = (a / c) \times 10^{(b-d)}$. Again, ensure the resulting $a$ value is between 1 and 10.
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• Adjusting the Exponent: If multiplying or dividing results in an $a$ value outside the range of 1 to 10, move the decimal place and adjust the exponent. Moving the decimal to the left increases the exponent, and moving it to the right decreases the exponent.
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• Example: $(2 \times 10^3) \times (3 \times 10^4) = 6 \times 10^7$ and $(8 \times 10^6) / (2 \times 10^2) = 4 \times 10^4$

Practice Quiz

1. What is $(2 \times 10^4) \times (3 \times 10^5)$?
1. $5 \times 10^9$
2. $6 \times 10^9$
3. $5 \times 10^{20}$
4. $6 \times 10^{20}$
2. What is $(8 \times 10^8) / (4 \times 10^2)$?
1. $2 \times 10^4$
2. $2 \times 10^6$
3. $32 \times 10^{10}$
4. $12 \times 10^{6}$
3. Simplify $(5 \times 10^3) \times (7 \times 10^{-7})$
1. $3.5 \times 10^{-3}$
2. $35 \times 10^{-4}$
3. $3.5 \times 10^{-4}$
4. $12 \times 10^{-4}$
4. What is $(9 \times 10^{-2}) / (3 \times 10^{-5})$?
1. $3 \times 10^{-7}$
2. $3 \times 10^{-3}$
3. $3 \times 10^{3}$
4. $27 \times 10^{-7}$
5. Calculate $(1.2 \times 10^5) \times (5 \times 10^{-2})$
1. $6 \times 10^3$
2. $6 \times 10^7$
3. $6 \times 10^{-10}$
4. $6.2 \times 10^3$
6. What is $(4.8 \times 10^{-4}) / (1.6 \times 10^{-6})$?
1. $3 \times 10^{-2}$
2. $3 \times 10^{-10}$
3. $3 \times 10^{2}$
4. $7.68 \times 10^{-10}$
7. Evaluate $(2.5 \times 10^{-3}) \times (4 \times 10^{-3})$
1. $1 \times 10^{-6}$
2. $1 \times 10^0$
3. $1 \times 10^{-9}$
4. $10 \times 10^{-6}$