Number Foundations practice questions — Honors Math

The second decimal is $6 \ge 5$, so the first decimal rounds up: $4.9 \to 5.0$ (the $9$ carries to give $5.0$).

$0.2 = \dfrac{2}{10} = \dfrac{1}{5}$.

$49.2 \approx 50$ and $5.1 \approx 5$, so the estimate is $50 \times 5 = 250$.

$\dfrac{3}{5} = 0.6$ and $58\% = 0.58$.

Since $0.6 > 0.58 > 0.55$, the largest is $\dfrac{3}{5}$.

$6 = 2 \cdot 3$ and $8 = 2^3$.

Highest powers: $2^3$ and $3$.

$\text{LCM} = 8 \cdot 3 = 24$.

$3 \times 4 = 12$, then $2 + 12 = 14$.

$(5 + 1)^2 = 6^2 = 36$, then $36 \div 4 = 9$.

$3 + 4 = 7$; $2 \times 7 = 14$; $20 - 14 = 6$.

The third decimal digit is $8 \ge 5$, so round the second decimal up: $3.728 \approx 3.73$.

$51 = 3 \cdot 17$, $57 = 3 \cdot 19$, $63 = 7 \cdot 9$.

$59$ has no factor up to $\sqrt{59} < 8$, so $59$ is prime.