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Exponents and scientific notation — SHSAT practice questions

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Practice 113 Exponents and scientific notation questions in the app

What this topic is

Exponents and scientific notation on the SHSAT Mathematics section covers products and quotients of powers with a common base and the conversion, multiplication, and comparison of numbers in scientific notation.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

What is $(4.0\times10^{5})(3.0\times10^{-2})$ in scientific notation?

A$1.2\times10^{3}$✗ Not this oneB$7.0\times10^{3}$✗ Not this oneC$1.2\times10^{4}$✓ CorrectD$1.2\times10^{7}$✗ Not this one

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Answer: C — $1.2\times10^{4}$

Multiply coefficients and add exponents: $4.0\times3.0=12.0$ and $5+(-2)=3$, so $12.0\times10^{3}=1.2\times10^{4}$.

Question 2Easier

What is $\dfrac{2^5\cdot2^3}{2^4}$?

A4✗ Not this oneB8✗ Not this oneC16✓ CorrectD32✗ Not this one

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Answer: C — 16

Combining exponents gives $2^{5+3-4}=2^4=16$.

Question 3Easier

Four engineering tolerances are listed in scientific notation. Which listed value is greatest?

A$1.4\times10^{5}$✓ CorrectB$6.2\times10^{4}$✗ Not this oneC$8.9\times10^{3}$✗ Not this oneD$9.5\times10^{2}$✗ Not this one

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Answer: A — $1.4\times10^{5}$

Compare powers of 10 first. The greatest exponent dominates here, so $1.4\times10^{5}$ is largest.

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