Metric Conversions & Scientific Notation
Name:_________________________
Date: _________________
Below is a table demonstrating equal values of the same measurement (first example: 1.30 m = 130 cm)
Please fill in the open spaces in the table. You should be thinking about “how” the decimal point changes as
you move between the units (all changing by a factor of 10 – one decimal place.
Length (m)
Volume (L)
Mass (g)
kilo (k)
0.0013 km
0.0001645 kL
0.068 kg
hecto (h)
deca (da)
0.013 hm
0.13 dam
0.001645 hL
0.01645 daL
0.68 hg
6.8 dag
(base unit)
1.30 m
0.1645 L
deci (d)
13.0 dm
1.645 dL
centi (c)
130 cm
milli (m)
1300 mm
257.0 cm
4.91 g
68 g
72.3 dL
680 dg
16.45 cL
6800 cg
164.5 mL
68000 mg
1) 38.7 m = ___________ km
2) 450 mg = ___________ cg
3) 1.2 kL = ____________ mL
4) 2.54 cm = ___________ mm
5) 0.4536 kg = ___________ g
6) 79.2 cL = ____________ L
1)
kilo (k)
hecto (h)
deca (da)
(base unit)
deci (d)
centi (c)
milli (m)
1) 38.7 m
2) 450 mg
3) 1.2 kL
4) 2.54 cm
1.2 kL
5) 0.4536 kg
6) 79.2 cL
.4536 kg
38.7 m
2.54 cm
79.2 cL
450 mg
HOMEWORK Problems – Metric Conversions
k
h
da B
d
c
m
7) 2471 cm = ___24.71___ m
10) 3.45 hL= _______ L
13) 84 cm = _______ mm
8) 0.00613 L = ______ mL
11) 0.23 hg = _______ cg
14) 1900 kg = _______ dg
9) 109 kg = _______ g
12) 0.0062 cm = _______ m
15) 22.6 dam = _______ hm
Scientists have developed a shorter method to express very large or very small numbers. This method is
called scientific notation. Scientific Notation is based on powers of the base number 10.
104
10000
103
1000
102
100
101
10
100
1
In scientific notation all numbers are written like this:
Examples)
10-1
.1
10-2
.01
a × 10b
3.654 x
4.31 x
5.9 x
6.52 x
10-3
.001
10-4
.0001
("a times ten to the power of b"),
102 =
104 =
10-1 =
10-3 =
365.4
43100
0.59
0.00652
Note: For each “a” value, there is only a single digit followed by the decimal
PRACTICE PROBLEMS: Convert each of the numbers below from scientific notation to standard form.
You should use your calculator to CHECK your answers.
1) 7.8613 x 102
=
3) 3.691 x 10-2
5) 1.37 x 10-4
=
=
7) 2.8 x 101 =
____________
____________
____________
____________
9) 4.21 x 106 =
____________
2)
9.5314 x 103
=
4)
2.3 x 10-3
____________
6)
6.41 x 104
=
____________
8)
5.56 x 100
=
____________
10)
=
9.08 x 103
=
____________
____________
PRACTICE PROBLEMS: Convert each of the numbers below from standard form to scientific notation.
11) 685
=
13) 0.156
15) 4736.2
17) 56 =
____________
=
=
____________
____________
____________
19) .00000864 =
____________
12)
2760
=
____________
14)
0.0092
16)
64.12
18)
1.23 =
20)
17,200,000
=
=
____________
____________
____________
=
____________
HOMEWORK PROBLEMS: For each of the homework problems on the reverse page (Metric Conversions),
convert each number from standard form to scientific notation. (Remember, how to check your answers)
7) 2471 cm = ___24.71___ m
2.471 x 103 cm
2.471 x 101 m
10) 3.45 hL= _______ L
3.45 x 100 hL
13) 84 cm = _______ mm
8.4 x 101 cm
Measurements with Significant Figures
Name: ______________________
Date: ____________________
1) Determine the length of each line (with UNITS). Record your answer to the correct number of sig figs
a)
b)
c)
0
a) =
b) =
c) =
2) How do you determine the correct number of significant figures (sig figs) in a measurement?
3) Is it okay to make an estimate when measuring something? EXPLAIN your answer.
Determine the measurement of each item below (with correct UNITS and correct significant figures)
4)
6)
7)
8)
9)
5)
Write the measurement of each item in both standard form (sf) and in scientific notation (sn)
All answers MUST include the proper Units:
4)
(sf)
_____________
(sn)
_________________
7) (sf) ______________
(sn)
_________________
5)
(sf)
_____________
(sn)
_________________
8) (sf) ______________
(sn)
_________________
6)
(sf)
_____________
(sn)
_________________
9) (sf) ______________
(sn)
_________________
Counting Significant Figures (Sig Figs)
Name: ________________________
Date:_____________
RULE -1: If the decimal is Present: Find the first non zero on the left, then count all digits to the RIGHT
If the decimal is Absent: Find the first non zero on the right, then count all digits to the LEFT
RULE-2: Every digit in scientific notation is Significant
RULE-3: Any number that is counted is an EXACT number and has UNLIMITED significant digits.
Practice Problems: Identify the number of significant digits in each of the following
1) 23.7 x 10-2 cm
2) 1.4 x 107 L
3) 4.293 x 104 km 4) 705 seconds
5) 600 cm
6) 4301.0 GHz
7) 0.00056 dg
8) 40280 daL
10) 8 students
9) 24 Megapixels
MORE Practice Problem: Identify the number of significant digits in each of the following
1) 192 rulers
2) 5,400 km
3) 100.0 minutes
4) 7.29 years
5) 0.000004 m
6) 8,000,000 m/s
7) 0.010060 hL
8) 10.02 cg
9) 52 teeth
10) 357 dam
EVEN MORE Practice Problem: Identify the number of significant digits in each of the following
1) 409 cars
2) 51.050 L
3) 0.000007
4) 6.52 x 10-5 kg
5) 5,000 staples
6) 738.000 Mm
7) 7.20 x 108 kL
8) 31 light years
9) 30 m
10) 16
NOTE: Use the following information to answer questions # 21 and # 22 on the back side of this page:
Determining Accuracy: Compare the accepted (true) value to the AVERAGE of the experimental trials
Determining Precision: Subtract the lowest measurement from the highest measurement
HOME WORK - How many significant figures are in each of the following numbers?
NOTE: Be careful of the units, some of them are TRICKY 
11)
1.2 x 103 mice ____
210 seconds ____
12)
0.00120 minutes ____
3)
801.5 kg ____
13)
30.0 L ____
4)
4,000 mm ____
14)
9.010 x 10-6 kg ____
5)
101.0100 kL ____
15)
2,370.0 light years ____
6)
11 dogs ____
16)
6.200 x 10-4 km ____
7)
27 dag ____
17)
18 GHz
8)
1500 rulers ____
18)
27
9)
.0007 km ____
19)
3 x 100 m ____
10)
0.0300 mL ____
20)
200. L ____
1)
5.40 m
2)
____
____
____
Students were asked to determine the concentration (M) of acetic acid in a brand of barbeque sauce. The
results of three of the students are in the table below:
Andy
0.102 M
0.104 M
0.100 M
Trial -1
Trial -2
Trial -3
Brenda
0.097 M
0.094 M
0.10 M
Curt
0.0960 M
0.109 M
0.118 M
Average
21) If the accepted (true) concentration of acetic acid is 0.096 M, which student was the most precise?
Explain your answer.
22) If the accepted (true) concentration of acetic acid is 0.096 M, which student was the most accurate?
Explain your answer.
23) What is wrong with Brenda’s third measurement of 0.10 M?
24) What is wrong with Curt’s first measurement of 0.0960 M?
25) Calculate the error and percent error for Andy if the accepted (true) concentration is 0.096 M
Practice Worksheet for Calculations and Conversions
Name: ____________________
Date: _______________
Perform the following calculations and round to the correct number of significant figures.
1) 13.7 x 2.5 =
2) 200 x 3.58 =
3) 0.00003 x 727 =
4) 5003 / 3.781 =
5) 89 / 9.0 =
6) 5000 / 55 =
xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxx
1) 4.60 + 3 =
2) 0.008 + 0.05 =
3) 22.4420 + 56.981 =
4) 200 - 87.3 =
5) 67.5 - 0.009 =
6) 71.86 - 13.1 =
Part I. Change the following numbers to proper scientific notation
1) 65.7 = ________________
2) 0.00545 = _____________
3) 22 450 000 = _____________
Part II. Change the following numbers to standard notation
4) 8.85 x 104 =____________
5) 1.847 x 102 =____________
6) 3.400 x 10-3 =____________
1. Calculate the density of a material that has a mass of 52.457 g and a volume of 13.5 cm3.
2. A student finds a rock on the way to school. In the laboratory he determines that the volume of the
rock is 22.7 cm3, and the mass in 39.943 g. What is the density of the rock?
3. If 30.943 g of a liquid occupy a space of 35.0 ml, what is the density of the liquid in g/cm3?
1) 250 Kelvin =
____°C
2) 339 Kelvin =
____°C
3) 17 Celsius =
____ K
4) 55 Celsius =
____K
More Practice Problems
Perform the following calculations and round to the correct number of significant figures.
1) 50.0 x 2.00 =
2) 2.3 x 3.45 x 7.42 =
3) 1.0007 x 0.009 =
4) 51 / 7 =
5) 208 / 9.0 =
6) 0.003 / 5 =
1) 357.89 + 0.002 =
2) 17.95 + 32.42 + 50 =
3) 5.5 + 3.7 + 2.97 =
4) 84.675 - 3 =
5) 75 - 2.55 =
6) 10 - 9.9 =
Part I. Change the following numbers to proper scientific notation:
1) 0.0803 = ________________ 2) 678.3 = _______________
3) 3 450 000= ______________
Part II. Change the following numbers to standard notation:
4) 6.5 x 10-2 = _____________
5) 9.7 x 102 = __________
6) 1.4 x 10-1 = ______________
1. The mass of a toy spoon is 7.5 grams, and its volume is 3.2 ml. What is the density of the toy
spoon?
2. A mechanical pencil has the density of 3 grams per cubic centimeter. The volume of the pencil is
15.8 cubic centimeters. What is the mass of the pencil?
3. A screwdriver has the density of 5.5 grams per cubic centimeter. it also has the mass of 2.3 grams.
What is the screwdrivers volume?
1) 304.5 Kelvin =
___°C
2) 172 Kelvin =
____°C
3) 126 Celsius =
____ K
4) -8 Celsius =
____K