Question

question 1
using the table of equalities, determine which choice contains equivalent measurements.
metric and si prefixes
prefix symbol numerical value scientific notation equality
prefixes that increase the size of the unit
peta p 1 000 000 000 000 000 $10^{15}$ 1 pg = $10^{15}$g 1 g = $10^{-15}$pg
tera t 1 000 000 000 000 $10^{12}$ 1 tg = $10^{12}$g 1 g = $10^{-12}$tg
giga g 1 000 000 000 $10^{9}$ 1 gm = $10^{9}$m 1 m = $10^{-9}$gm
mega m 1 000 000 $10^{6}$ 1 mg = $10^{6}$g 1 g = $10^{-6}$mg 1 km = $10^{3}$m 1 m = $10^{-3}$km
kilo k 1 000 $10^{3}$
prefixes that decrease the size of the unit
decı d 0.1 $10^{-1}$ 1 dl = $10^{-1}$l 1 l = 10 dl
centi c 0.01 $10^{-2}$ 1 cm = $10^{-2}$m 1 m = 100 cm
milli m 0.001 $10^{-3}$ 1 ms = $10^{-3}$s 1 s = $10^{3}$ms
micro μ 0.000 001 $10^{-6}$ 1 μg = $10^{-6}$g 1 g = $10^{6}$μg
answer
1 g = 100 mg
1000 μg = 1 g
10 cg = 1 mg
0.01 dg = 1 cg
1 kg = 1×$10^{5}$ cg
i dont know yet

Explanation:

Step1: Recall metric - prefix conversion rules

We know that $1\ g = 10^{3}\ mg$, $1\ g=10^{6}\ \mu g$, $1\ mg = 10^{3}\ cg$, $1\ dg=10^{1}\ cg$, $1\ kg = 10^{3}\ g$ and $1\ g=10^{2}\ cg$, so $1\ kg=10^{3}\times10^{2}\ cg = 1\times10^{5}\ cg$.

Step2: Check each option

• Option 1: $1\ g = 100\ mg$ is incorrect as $1\ g = 10^{3}\ mg$.
• Option 2: $1000\ \mu g=1\ g$ is incorrect as $1\ g = 10^{6}\ \mu g$.
• Option 3: $10\ cg = 1\ mg$ is incorrect as $1\ mg=10^{3}\ cg$.
• Option 4: $0.01\ dg = 1\ cg$ is correct since $1\ dg = 10^{1}\ cg$, so $0.01\ dg=\frac{1}{100}\times10\ cg = 1\ cg$.
• Option 5: $1\ kg=1\times10^{5}\ cg$ is correct as $1\ kg = 10^{3}\ g$ and $1\ g = 10^{2}\ cg$, so $1\ kg=10^{3}\times10^{2}\ cg=1\times 10^{5}\ cg$.

Answer:

D. $0.01\ dg = 1\ cg$, E. $1\ kg=1\times10^{5}\ cg$