Question

instructions. show all work using dimensional analysis. identify the statement of equality that you used to solve the problem (see the equalities table below) and calculate the final answer.
example problem:
● convert 18 centimeters into meters. equality: 1 centimeter = 0.01 m
18 cm×\frac{0.01 m}{1 cm}=0.18 m

1. convert 6 540 millimeters into meters. (use 1 mm = 0.001 m)
2. convert 185 decimeters into meters. (use 1 dm = 0.1 m)
3. convert 3.3 kilograms into grams. (use 1 kg = 1000 g)
4. convert 876 decigrams into grams.
5. convert 0.035 grams into kilograms.
6. convert 7.7 m into centimeters.
7. convert 94.2 meters into decimeters.
8. convert 0.087 m into millimeters.
9. convert 4.1 nanometers into meters.
10. how many gigameters is 8.5×10¹⁰ meters?

si prefixes
prefix symbol meaning multiply unit by
giga- g billion (10⁹) 1,000,000,000
mega- m million (10⁶) 1,000,000
kilo- k thousand (10³) 1000
deci- d tenth (10⁻¹) 0.1
centi- c hundredth (10⁻²) 0.01
milli- m thousandth (10⁻³) 0.001
micro- μ millionth (10⁻⁶) 0.000001
nano- n billionth (10⁻⁹) 0.000000001

Explanation:

Step1: Convert 6540 mm to m

Use the equality $1\ mm = 0.001\ m$. So, $6540\ mm\times\frac{0.001\ m}{1\ mm}=6.54\ m$

Step2: Convert 185 dm to m

Use the equality $1\ dm = 0.1\ m$. So, $185\ dm\times\frac{0.1\ m}{1\ dm}=18.5\ m$

Step3: Convert 3.3 kg to g

Use the equality $1\ kg = 1000\ g$. So, $3.3\ kg\times\frac{1000\ g}{1\ kg}=3300\ g$

Step4: Convert 876 dg to g

Use the equality $1\ dg = 0.1\ g$. So, $876\ dg\times\frac{0.1\ g}{1\ dg}=87.6\ g$

Step5: Convert 0.035 g to kg

Use the equality $1\ kg = 1000\ g$. So, $0.035\ g\times\frac{1\ kg}{1000\ g}=3.5\times 10^{-5}\ kg$

Step6: Convert 7.7 m to cm

Use the equality $1\ m = 100\ cm$. So, $7.7\ m\times\frac{100\ cm}{1\ m}=770\ cm$

Step7: Convert 94.2 m to dm

Use the equality $1\ m = 10\ dm$. So, $94.2\ m\times\frac{10\ dm}{1\ m}=942\ dm$

Step8: Convert 0.087 m to mm

Use the equality $1\ m = 1000\ mm$. So, $0.087\ m\times\frac{1000\ mm}{1\ m}=87\ mm$

Step9: Convert 4.1 nm to m

Use the equality $1\ nm = 10^{-9}\ m$. So, $4.1\ nm\times\frac{10^{-9}\ m}{1\ nm}=4.1\times 10^{-9}\ m$

Step10: Convert $8.5\times 10^{10}$ m to Gm

Use the equality $1\ Gm = 10^{9}\ m$. So, $8.5\times 10^{10}\ m\times\frac{1\ Gm}{10^{9}\ m}=85\ Gm$

Answer:

1. $6.54\ m$
2. $18.5\ m$
3. $3300\ g$
4. $87.6\ g$
5. $3.5\times 10^{-5}\ kg$
6. $770\ cm$
7. $942\ dm$
8. $87\ mm$
9. $4.1\times 10^{-9}\ m$
10. $85\ Gm$