UTMA Number Theory and Arithmetic 3

Question 1

What is the result of (−3)³?

Accepted Answer

−27

Answer

(−3)³ = (−3)(−3)(−3) = 9 × (−3) = −27.

Question 2

Which of the following is an irrational number?

Accepted Answer

√7

Answer

√7 cannot be expressed as a ratio of integers, so it is irrational.

Question 3

What is 3/8 expressed as a decimal?

Accepted Answer

0.375

Answer

3 ÷ 8 = 0.375.

Question 4

How many zeros are at the end of 20!?

Accepted Answer

4

Answer

Trailing zeros come from factors of 10 = 2×5; count factors of 5: ⌊20/5⌋ + ⌊20/25⌋ = 4 + 0 = 4.

Question 5

What is the remainder when 2²⁰ is divided by 3?

Accepted Answer

1

Answer

Since 2 ≡ −1 (mod 3), 2²⁰ ≡ (−1)²⁰ = 1 (mod 3).

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