Exponents, powers, roots; scientific notation — ISEE Upper practice questions

What this topic is

Exponents, powers, roots; scientific notation on ISEE Upper Mathematics Achievement covers converting a number written as a coefficient times a power of ten into ordinary decimal form, evaluating expressions that mix a zero exponent with a negative exponent, and locating a square root between two consecutive integers.

Sample questions

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

Question 1Easier

Which decimal is equivalent to $7.5\times10^{-3}$?

A0.00075✗ Not this oneB0.0075✓ CorrectC0.075✗ Not this oneD7500✗ Not this one

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Answer: B — 0.0075

Multiplying by $10^{-3}$ moves the decimal three places left. Therefore $7.5\times10^{-3}=0.0075$.

Question 2Easier

Between which two consecutive integers is $\sqrt{70}$?

A7 and 8✗ Not this oneB8 and 9✓ CorrectC9 and 10✗ Not this oneD10 and 11✗ Not this one

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Answer: B — 8 and 9

Since $8^2=64$ and $9^2=81$, and 70 is between 64 and 81, $\sqrt{70}$ is between 8 and 9.

Question 3Easier

What is the value of $5^0+2^{-2}$?

A$\dfrac{5}{4}$✓ CorrectB$\dfrac{1}{4}$✗ Not this oneC$\dfrac{21}{4}$✗ Not this oneD$\dfrac{3}{4}$✗ Not this one

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Answer: A — $\dfrac{5}{4}$

Since $5^0=1$ and $2^{-2}=\dfrac{1}{4}$, the sum is $1+\dfrac{1}{4}=\dfrac{5}{4}$.

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