Chem 1020
Homework 1
Answer key
1. The number 0.005802 expressed in scientific notation is:
To convert this number to scientific notation, the decimal point must be moved so
that there is one digit (1-9) to the left of the decimal point. So moving the decimal
point 3 places to the right makes the number 5.802. Then to make this equivalent to
the original number given, it must be multiplied by a power of 10. Moving 3 places
to the right is equivalent to multiplying the number by 10-3. So, the number in
scientific notation is 5.802 x 10-3. Choice D is correct.
2. What is the result of the following multiplication expressed in scientific
notation to the correct number of significant figures?
(2.08 x 105)(7.0 x 10-5)
This could be solved two ways. Entering it in the calculator will give you an answer
you must convert into scientific notation. Typing the following in the calculator,
2.08 E 5 x 7.0 E -5 = 14.56. In scientific notation, this is 1.456 x 101, but this does
not have the correct number of significant figure. When multiplying the answer may
only have as many significant figures as the value you entered in the calculation
with the fewest sig. figs. In this case, 2.08 x 105 has 3 sig figs (the power of 10
makes no difference on sig. figs.) and 7.0 x 10-5 has 2 sig figs. Therefore, the
answer must be rounded to 2 sig figs: 1.456 x 101 becomes 1.5 x 101. Choice C is
correct.
You could have also multiplied just the numbers and then dealt with the powers of
10 separately. 2.08 x 7.0 =14.56, and 105 x 10-5 = 10(5-5) = 100, so the product of the
two is 14.56 x 100, but this is 1.456 x 101 in correct scientific notation. Rounding to
the correct number of sig figs as above gives 1.5 x 101, or choice C.
3. Convert 256 L to milliliters.
Since "milli" or just "m" is the SI prefix which means 10-3, we can say that
1 mL = 10-3 L (simply by replacing the "m" prefix with its equivalent power of 10).
So, in dimensional analysis, we start with the known quantity and apply a
conversion factor so the units cancel.
258 L "
!
1 mL
= 258 "10 3 mL = 2.58 "10 5 mL (choice E)
-3
10 L
4. 275 °F is equivalent to:
We use the equation to convert between °F and °C, as shown on our conversion
sheets:
T°C = 59 (T°F " 32)
= 59 (275 °F " 32)
= 59 (243)
= 135 °C, (choice B)
!
5. The density of copper is 8.92 g/mL. The mass of a piece of copper that has a
volume of 10.0 mL is:
Since density =
mass
, we can rearrange the equation to solve for mass:
volume
m
(multiply both sides by v to get m by itself)
v
! vd = "$ m %'v (the v's on top and bottom of the right side cancel)
#v&
vd = m = (10.00 mL)(8.92 g/mL)
m = 89.2 g (choice C)
d=
!