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

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. Students must apply exponent rules and estimate roots without a calculator. Items are short multiple-choice stems whose options are decimals, integer pairs, or simplified values. Traps include shifting the decimal the wrong way for a negative exponent, treating a negative exponent as a signed number, and picking integers that do not sit immediately beside the root.

  • Section: Mathematics Achievement 47 questions on the paper
  • 118 practice questions in the app

Sample questions

Question 1

Which decimal is equivalent to 7.5×10−37.5\times10^{-3}?

  1. A0.00075
  2. B0.0075
  3. C0.075
  4. D7500
Show answer

Answer: B — 0.0075

Multiplying by 10−310^{-3} moves the decimal three places left. Therefore 7.5×10−3=0.00757.5\times10^{-3}=0.0075.

Question 2

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

  1. A7 and 8
  2. B8 and 9
  3. C9 and 10
  4. D10 and 11
Show answer

Answer: B — 8 and 9

Since 82=648^2=64 and 92=819^2=81, and 70 is between 64 and 81, 70\sqrt{70} is between 8 and 9.

Question 3

What is the value of 50+2−25^0+2^{-2}?

  1. A54\dfrac{5}{4}
  2. B14\dfrac{1}{4}
  3. C214\dfrac{21}{4}
  4. D34\dfrac{3}{4}
Show answer

Answer: A — 54\dfrac{5}{4}

Since 50=15^0=1 and 2−2=142^{-2}=\dfrac{1}{4}, the sum is 1+14=541+\dfrac{1}{4}=\dfrac{5}{4}.

Practice 118 Exponents, powers, roots; scientific notation questions in the app

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