Question

make the following conversions
a. 15.6 g =? μg
b. 3.72 x 10⁴ g =? kg
c. 72.3 l =? cm³
d. 3.7x10² j =? kj
e. 4.7x10⁵ mg =? dg
f. 8.1 x 10⁻⁴ dl =? μl
g. 3.7x10² g =? pg
h. 4.7x10⁶ mg =? μg
i. 6.1 x 10⁻³ dl =? ml
j. 25.6 g =? mg
k. 5.72 x 10⁴ l =? ml
l. 1.45 x 10⁵ l =? cm³

1 lb = 454 g, 1 qt = 0.946 l, 1.6093km = 1 mile = 5280 feet

1. an ore is 3.5% copper by mass. how many kilograms of ore are needed to obtain 1.5 kilograms of copper?
2. calculate the volume in cubic centimeters of a gold bar with a mass of 1.5 kg.
3. a rock has a mass of 500 g and a volume of 200 cm3. what is its density in g/cm3?
4. a grain of salt has a mass of 0.1 mg how many grains of salt are in 5 lb of salt?
5. you pass a road sign saying

ew york 112 km\.
a. if you drive at a constant speed of 65 mi/h, how many hours will it take you to reach new york?
b. if your car gets 28 miles to the gallon, how many liters of gas are necessary to travel there?
c. fuel for the car is $8.93 x 10⁻³ per milliliter how much will it cost to make the drive there?

Explanation:

a. Convert 15.6 g to μg

1 g = 10⁶ μg. Multiply 15.6 by 10⁶.
$15.6\times10^{6}\text{ μg}=1.56\times 10^{7}\text{ μg}$

b. Convert $3.72\times 10^{4}$ g to kg

1 kg = 1000 g = 10³ g. Divide $3.72\times 10^{4}$ by 10³.
$\frac{3.72\times 10^{4}}{10^{3}}\text{ kg}=37.2\text{ kg}$

c. Convert 72.3 L to cm³

1 L = 1000 cm³. Multiply 72.3 by 1000.
$72.3\times1000\text{ cm}^3 = 72300\text{ cm}^3$

d. Convert $3.7\times 10^{2}$ J to kJ

1 kJ = 1000 J=10³ J. Divide $3.7\times 10^{2}$ by 10³.
$\frac{3.7\times 10^{2}}{10^{3}}\text{ kJ}=0.37\text{ kJ}$

e. Convert $4.7\times 10^{5}$ mg to dg

1 dg = 100 mg = 10² mg. Divide $4.7\times 10^{5}$ by 10².
$\frac{4.7\times 10^{5}}{10^{2}}\text{ dg}=4700\text{ dg}$

f. Convert $8.1\times 10^{-4}$ dL to μL

1 dL = 100000 μL = 10⁵ μL. Multiply $8.1\times 10^{-4}$ by 10⁵.
$8.1\times 10^{-4}\times10^{5}\text{ μL}=81\text{ μL}$

g. Convert $3.7\times 10^{2}$ g to pg

1 g = 10¹² pg. Multiply $3.7\times 10^{2}$ by 10¹².
$3.7\times 10^{2}\times10^{12}\text{ pg}=3.7\times 10^{14}\text{ pg}$

h. Convert $4.7\times 10^{6}$ mg to μg

1 μg = 0.001 mg=10⁻³ mg. Divide $4.7\times 10^{6}$ by 10⁻³.
$\frac{4.7\times 10^{6}}{10^{-3}}\text{ μg}=4.7\times 10^{9}\text{ μg}$

i. Convert $6.1\times 10^{-3}$ dL to mL

1 dL = 100 mL. Multiply $6.1\times 10^{-3}$ by 100.
$6.1\times 10^{-3}\times100\text{ mL}=0.61\text{ mL}$

j. Convert 25.6 g to mg

1 g = 1000 mg = 10³ mg. Multiply 25.6 by 10³.
$25.6\times10^{3}\text{ mg}=25600\text{ mg}$

k. Convert $5.72\times 10^{4}$ L to ML

1 ML = 1000000 L = 10⁶ L. Divide $5.72\times 10^{4}$ by 10⁶.
$\frac{5.72\times 10^{4}}{10^{6}}\text{ ML}=0.0572\text{ ML}$

l. Convert $1.45\times 10^{5}$ L to cm³

1 L = 1000 cm³. Multiply $1.45\times 10^{5}$ by 1000.
$1.45\times 10^{5}\times1000\text{ cm}^3=1.45\times 10^{8}\text{ cm}^3$

1. Let the mass of ore be $x$ kg. Given the ore is 3.5% copper by mass and we want 1.5 kg of copper.

We have the equation $0.035x = 1.5$. Solve for $x$.
$x=\frac{1.5}{0.035}\text{ kg}\approx42.86\text{ kg}$

1. The density of gold is $

ho = 19.32\text{ g/cm}^3$. First convert 1.5 kg to g: 1.5 kg = 1500 g.
Using the formula $
ho=\frac{m}{V}$, we can solve for $V$. $V=\frac{m}{
ho}=\frac{1500}{19.32}\text{ cm}^3\approx77.64\text{ cm}^3$

1. Given $m = 500$ g and $V = 200$ cm³. Using the density formula $

ho=\frac{m}{V}$.
$
ho=\frac{500}{200}\text{ g/cm}^3 = 2.5\text{ g/cm}^3$

1. First convert 5 lb to g: 5 lb = 5×454 g = 2270 g. Then convert to mg: 2270 g=2270000 mg.

The number of grains $n=\frac{2270000}{0.1}=22700000$

1. a. First convert 112 km to miles. 1 km = 0.621371 miles, so 112 km = 112×0.621371 miles≈69.6 miles.

Using the formula $t=\frac{d}{v}$, where $d$ is distance and $v$ is speed. $t=\frac{69.6}{65}\text{ h}\approx1.07\text{ h}$
b. The distance $d = 69.6$ miles. If the car gets 28 miles per gallon, the number of gallons $g=\frac{69.6}{28}$ gallons.
1 gallon = 3.78541 L. So the number of liters $L=\frac{69.6}{28}\times3.78541\text{ L}\approx9.4\text{ L}$
c. The volume of gas is 9.4 L = 9400 mL. The cost $C=8.93\times 10^{-3}\text{ dollars/mL}\times9400\text{ mL}\approx84\text{ dollars}$

Answer:

a. $1.56\times 10^{7}\text{ μg}$
b. 37.2 kg
c. 72300 cm³
d. 0.37 kJ
e. 4700 dg
f. 81 μL
g. $3.7\times 10^{14}$ pg
h. $4.7\times 10^{9}$ μg
i. 0.61 mL
j. 25600 mg
k. 0.0572 ML
l. $1.45\times 10^{8}$ cm³

1. 42.86 kg
2. 77.64 cm³
3. 2.5 g/cm³
4. 22700000
5. a. 1.07 h

b. 9.4 L
c. 84 dollars