Question

column a

1. d 50 l x ______ = 0.050 kl
2. g 22 g ______ = 2,200 cg
3. f 825 cm ______ = 0.00825 km
4. e 2,350 kg ______ = 2,350,000 g
5. a 19 ml ______ = 1.9 cl
6. __ 52 km ____ = 52,000 m
7. i 36 m ______ = 3,600 cm
8. □ 18 cm ______ = 180 mm
9. __ 6 g ____ = 6,000 mg
10. __ 4,259 ml ____ = 4.259 l

column b
b. $\frac{1000\text{mg}}{1\text{g}}$
c. $\frac{1\text{m}}{100\text{cm}}$
d. $\frac{1\text{kl}}{1000\text{l}}$
e. $\frac{1000\text{g}}{1\text{kg}}$
f. $\frac{1\text{m}}{100\text{cm}} \times \frac{1000\text{mm}}{1\text{m}}$
g. $\frac{100\text{cg}}{1\text{g}}$
h. $\frac{1\text{g}}{1000\text{mg}}$
i. $\frac{100\text{cm}}{1\text{m}}$
j. $\frac{1\text{m}}{100\text{cm}} \times \frac{1\text{km}}{1000\text{m}}$
k. $\frac{1000\text{m}}{1\text{km}^2}$ (note: likely typo, intended $1\text{km}$)
l. $\frac{1\text{l}}{1000\text{ml}} \times \frac{100\text{cl}}{1\text{l}}$

Explanation:

Question 8:

Step1: Recall unit conversion for km to m

We know that \(1\space km = 1000\space m\), so the conversion factor is \(\frac{1000\space m}{1\space km}\).

Step2: Apply the conversion factor

For \(52\space km\) to \(m\), we multiply by \(\frac{1000\space m}{1\space km}\), so \(52\space km\times\frac{1000\space m}{1\space km}=52000\space m\). Looking at Column B, option k is \(\frac{1000m}{1km}\).

Step1: Recall unit conversion for cm to mm

We know that \(1\space cm = 10\space mm\), so the conversion factor is \(\frac{10\space mm}{1\space cm}\).

Step2: Apply the conversion factor

For \(18\space cm\) to \(mm\), we multiply by \(\frac{10\space mm}{1\space cm}\), so \(18\space cm\times\frac{10\space mm}{1\space cm} = 180\space mm\). Wait, but looking at Column B, let's check the options. Wait, maybe I made a mistake. Wait, \(1\space cm=10\space mm\), so the conversion factor can also be thought as \(\frac{10\space mm}{1\space cm}\), but looking at the options, let's re - check. Wait, option c is \(\frac{1m}{100cm}\), no. Wait, option c is \(\frac{1m}{100cm}\), option i is \(\frac{100cm}{1m}\), option j is \(\frac{1m}{100cm}\times\frac{1km}{1000m}\), no. Wait, wait, \(1\space cm = 10\space mm\), so \(18\space cm=18\times10\space mm = 180\space mm\). Let's check the options in Column B. Wait, maybe the options are mis - labeled? Wait, no, let's check the given Column B. Wait, option c is \(\frac{1m}{100cm}\), option i is \(\frac{100cm}{1m}\), option j is \(\frac{1m}{100cm}\times\frac{1km}{1000m}\), option k is \(\frac{1000m}{1km}\), option l is \(\frac{1L}{1000mL}\times\frac{100cL}{1L}\). Wait, maybe I missed an option. Wait, the original problem's Column B: let's re - list Column B:

b. \(\frac{1000mg}{1g}\)

c. \(\frac{1m}{100cm}\)

d. \(\frac{1kL}{1000L}\)

e. \(\frac{1000g}{1kg}\)

f. \(\frac{1m}{100cm}\times\frac{1000mm}{1m}\)

g. \(\frac{100cg}{1g}\)

h. \(\frac{1g}{1000mg}\)

i. \(\frac{100cm}{1m}\)

j. \(\frac{1m}{100cm}\times\frac{1km}{1000m}\)

k. \(\frac{1000m}{1km}\)

l. \(\frac{1L}{1000mL}\times\frac{100cL}{1L}\)

Ah! Option f: \(\frac{1m}{100cm}\times\frac{1000mm}{1m}\). Let's simplify option f: \(\frac{1m}{100cm}\times\frac{1000mm}{1m}=\frac{1000mm}{100cm}=\frac{10\space mm}{1\space cm}\), which is the conversion factor for \(cm\) to \(mm\). So for \(18\space cm\) to \(mm\), we use the conversion factor \(\frac{10\space mm}{1\space cm}\), which is equivalent to option f. Wait, no, \(18\space cm\times\frac{10\space mm}{1\space cm}=180\space mm\). Let's check option f: \(\frac{1m}{100cm}\times\frac{1000mm}{1m}=\frac{1000mm}{100cm}=10\space mm/cm\), so yes, option f is the conversion factor. Wait, but earlier I thought maybe, but let's do it again. \(1\space m = 100\space cm\) and \(1\space m=1000\space mm\), so \(\frac{1m}{100cm}\times\frac{1000mm}{1m}=\frac{1000mm}{100cm}=10\space mm/cm\). So \(18\space cm\times\frac{10\space mm}{1\space cm}=180\space mm\). So the answer for question 10 is f \(\frac{1m}{100cm}\times\frac{1000mm}{1m}\)

Step1: Recall cm - mm conversion

We know \(1\space cm = 10\space mm\), and the conversion factor can be derived from \(1\space m = 100\space cm\) and \(1\space m = 1000\space mm\).

Step2: Identify the conversion factor

The conversion factor \(\frac{1m}{100cm}\times\frac{1000mm}{1m}=\frac{1000mm}{100cm}=10\space mm/cm\), which is used to convert \(18\space cm\) to \(mm\) (\(18\space cm\times10\space mm/cm = 180\space mm\)). This conversion factor is option f in Column B.

Answer:

k \(\frac{1000m}{1km}\)

Question 10: