Exponents and scientific notation — SHSAT practice questions

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. Students must apply exponent rules, rewrite a product so the coefficient stays in the proper range, and decide which listed value is greatest when powers of ten differ. Questions often ask for a simplified power, a product written in scientific notation, or the greatest of several listed measurements. Choices usually look like nearby powers or other scientific-notation forms, and traps include adding exponents instead of multiplying them or picking the largest coefficient without checking the exponent.

Section: Mathematics 57 questions on the paper
113 practice questions in the app

Sample questions

Question 1

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

A $1.2\times10^{3}$
B $7.0\times10^{3}$
C $1.2\times10^{4}$
D $1.2\times10^{7}$

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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 2

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

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Answer: C — 16

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

Question 3

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

A $1.4\times10^{5}$
B $6.2\times10^{4}$
C $8.9\times10^{3}$
D $9.5\times10^{2}$

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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.

Practice 113 Exponents and scientific notation questions in the app

Exponents and scientific notation — SHSAT practice questions

Sample questions

More SHSAT topics

Mathematics