Question

select the choice that best answers each question or completes each statement.

1. which of these series of units is ordered from smallest to largest?

(a) μg, cg, mg, kg
(b) mm, dm, m, km
(c) μs, ns, cs, s
(d) nl, ml, dl, cl

1. which answer represents the measurement 0.00428 g rounded to two significant figures?

(a) 4.28×10³ g
(b) 4.3×10³ g
(c) 4.3×10⁻³ g
(d) 4.0×10⁻³ g

1. an over - the - counter medicine has 325 mg of its active ingredient per tablet. how many grams does this mass represent?

(a) 325,000 g
(b) 32.5 g
(c) 3.25 g
(d) 0.325 g

1. if 10⁴ μm = 1 cm, how many μm³ = 1 cm³?

(a) 10⁴
(b) 10⁶
(c) 10⁸
(d) 10¹²

1. if a substance contracts when it freezes, its

(a) density will remain the same.
(b) density will increase.
(c) density will decrease.
(d) change in density cannot be predicted.

Explanation:

Step1: Recall metric - prefix order

The metric prefixes in order of increasing magnitude: micro ($\mu$) = $10^{- 6}$, centi (c) = $10^{-2}$, milli (m) = $10^{-3}$, deci (d) = $10^{-1}$, kilo (k) = $10^{3}$. For time, nano (n) = $10^{-9}$, micro ($\mu$) = $10^{-6}$, centi (c) = $10^{-2}$, second (s). For volume, nano (n) = $10^{-9}$, milli (m) = $10^{-3}$, deci (d) = $10^{-1}$, centi (c) = $10^{-2}$.
For option A: $\mu g=10^{-6}g$, $cg = 10^{-2}g$, $mg=10^{-3}g$, $kg = 10^{3}g$. The correct order from smallest to largest is $\mu g,mg,cg,kg$.
For option B: $mm = 10^{-3}m$, $dm=10^{-1}m$, $m = 1m$, $km = 10^{3}m$. This is in the correct order from smallest to largest.
For option C: $ns=10^{-9}s$, $\mu s = 10^{-6}s$, $cs=10^{-2}s$, $s = 1s$. The correct order from smallest to largest is $ns,\mu s,cs,s$.
For option D: $nL=10^{-9}L$, $mL = 10^{-3}L$, $dL=10^{-1}L$, $cL=10^{-2}L$. The correct order from smallest to largest is $nL,mL,cL,dL$. So the answer to question 1 is B.

Step2: Rounding significant - figures

The number is $0.00428g$. The first non - zero digit is 4. To round to two significant figures, we look at the third digit. Since 8 > 5, we round up the second digit. $0.00428\approx4.3\times10^{-3}g$. So the answer to question 2 is C.

Step3: Unit conversion

We know that $1g = 1000mg$ or $1mg=\frac{1}{1000}g = 10^{-3}g$. Given $325mg$, then $325mg=325\times10^{-3}g = 0.325g$. So the answer to question 3 is D.

Step4: Volume unit conversion

If $10^{4}\mu m = 1cm$, then $(10^{4}\mu m)^{3}=(1cm)^{3}$. Using the power - of - a - power rule $(a^{m})^{n}=a^{mn}$, we have $(10^{4})^{3}\mu m^{3}=1cm^{3}$, and $(10^{4})^{3}=10^{12}$. So $10^{12}\mu m^{3}=1cm^{3}$. The answer to question 4 is D.

Step5: Density formula application

The density formula is $
ho=\frac{m}{V}$, where $
ho$ is density, $m$ is mass, and $V$ is volume. When a substance contracts (volume $V$ decreases) upon freezing and the mass $m$ remains constant (mass is conserved), according to the formula $
ho=\frac{m}{V}$, as $V$ decreases and $m$ is constant, $
ho$ increases. So the answer to question 5 is B.

Answer:

1. B. mm, dm, m, km
2. C. $4.3\times10^{-3}g$
3. D. $0.325g$
4. D. $10^{12}$
5. B. density will increase.