Name ___________________________________
Chemistry
Mr. Harper
Sig Fig Packet
Measurement Unit Study Guide
1. Significant figures and measurements
a. What is the difference between accuracy and precision? Why are both important in science?
b. What is a significant figure, and what are they used for?
c. How do you determine the number of sig figs in a number or measurement?
d. How do you round to the correct number of sig figs when multiplying, dividing, adding, or
subtracting?
e. How do you precisely read a triple beam balance, ruler, graduated cylinder, etc.?
2. Scientific notation
a. How do you convert a number into scientific notation and vice versa?
b. How do you multiply and divide numbers in scientific notation?
3. Conversion factors
a. How do you convert from one unit to another?
4. The mole
a. What is the mole, and how do chemists use it?
b. What is Avogadro’s number?
c. What is the molar mass of an element?
d. How do you convert among atoms, moles, and grams of an element?
1
Rules for Significant Figures
The following applies for numbers that are measured:
1) All non-zero digits in a number are significant.
a. A non-zero digit is any digit not zero: 1,2,3,4,5,6,7,8, and 9.
2) All leading zeros are not significant.
a. Leading zeros are the zeros in front of a number (on the left side). For example, the
number 0.00236 has 3 leading zeros in front of 236. These zeros are not significant.
3) Trailing zeros are significant only if a decimal point is present somewhere in the number.
a. Trailing zeros are the zeros at the end of a number (on the right side). For example, the
number 2000 has 3 trailing zeros.
b. For example, the zeros in 25.0 and 1.300 are significant because a decimal point is
present in both cases.
c. The zeros in 350 and 1000 are not significant because a decimal point is not present in
both cases.
d. The trailing zeros in 0.00420 and 800. are significant because a decimal point is present
in both cases.
4) Any zero between two other significant digits is always significant.
a. For example, all of the zeros in 801 and 10.05 are significant.
5) A line over a zero indicates that it is significant.
_
a. For example, there are 3 sig figs in 3500. The last zero (in the ones place) is not
significant.
6) When multiplying or dividing, the answer will have the same amount of sig figs as the value with the
least number of sig figs. If the answer has too many decimal places, round to the number of sig figs it
should have.
a. For example, 12 / 3.00 = 4  4.0
i. 12 has two significant figures and 3.00 has three, so the answer should only have two.
b. For example, 3.20 x 5.04 = 16.128  16.1
i. The starting values only have three significant figures each, so round the answer to three
significant figures, 16.1.
2
7) When adding and subtracting values, find the smallest decimal place that all values have in common and
are significant and that is the last significant decimal place in your answer. Add the values like normal
and round to the significant decimal place.
c. For example, 5.23 (significant to hundredths place)
+ 3.484 (significant to thousandths place)
8.714  8.71
i. The answer is limited to the hundredths place because 5.23, so the answer is rounded to
8.72 (hundredths place).
d. For example, 1050 (significant to tens place)
-326
(significant to ones place)
724  720
i. The answer is limited to the tens place because of 1050, so the answer is rounded to 720
(tens place).
8) When performing a calculation that involves only multiplication or division, do the whole calculation
and round at the end. Do not do any intermediate rounding.
9) When performing a calculation that involves only addition or subtraction, do the whole calculation and
round at the end. Do not do any intermediate rounding.
10) When performing a calculation that involves both multiplication or division and addition or subtraction,
you must round in between steps. That is, you must round between moving from a multiplication or
division step to an addition or subtraction step.
Practice: Determine the number of significant figures in the following measurements.
1) 0.0042 m
_____
10) 0.3 s
_____
19) 1000 m
_____
2) 900 mL
_____
11) 0.056 mL
_____
20) 0.00007 g
_____
3) 1.00 ms
_____
12) 800.01 g
_____
21) 1000.00 ms
_____
4) 3.50 g
_____
13) 0.0840 m
_____
22) 34,500 mg
_____
5) 5009 mm
_____
14) 173 ms
_____
23) 0.00302 cm
_____
6) 40.0 L
_____
15) 1.5000 kg
_____
24) 0.02070 mm _____
7) 300. mg
_____
16) 6.70001 s
_____
25) 20,005 kg
_____
8) 20900 cm
_____
17) 1000 m
_____
26) 680 g
_____
9) 102.0 km
_____
18) 1000. m
_____
27) 540.0 s
_____
3
Rules for rounding
When making calculations with measured values, the answer will need to be rounded to the correct
number of significant figures according to the following rules.
1) Round down whenever the digit following the last significant figure is a 0,1,2,3, or 4.
a. For example, 30.24 becomes 30.2.
2) Round up whenever the digit following the last significant figure is a 6,7,8,9 or a 5 with any
nonzero digit at any place after it.
a. For example, 22.49 becomes 22.5.
b. For example, 54.7511 round to the tenths place becomes 54.8.
3) If the digit following the last significant figure is a 5 with either zeros or nothing after it, round
to the even number.
a. For example, 79.3500 rounded to the tenths place becomes 79.4. The value is rounded
up to the even number.
b. For example, 32.65 becomes 32.6. The value is rounded down to the even number 6
instead of up to 7.
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Practice: Round the value to the given number of significant figures (SF).
1. 8.37; 2 SF
15. 0.427; 2 SF
2. 14.8; 2 SF
16. 1.7990; 3 SF
3. 1.4751; 3 SF
17. 13.5; 2 SF
4. 0.0765; 2 SF
18. 128.5; 3 SF
5. 285.35; 4 SF
19. 3.45; 2 SF
6. 10.1; 2 SF
20. 3.50001; 1 SF
7. 0.82396; 4 SF
21. 1850; 2 SF
8. 120.4; 3 SF
22. 21.58; 3 SF
9. 51382.4; 3 SF
23. 3.7148; 3 SF
10. 4.500; 1 SF
24. 116.0503; 4 SF
11. 1980; 1 SF
25. 2554.6; 3 SF
12. 173; 2 SF
26. 12.425; 4 SF
13. 17.4297; 3 SF
27. 0.025801; 1 SF
14. 23187; 2 SF
28. 14.69501; 4 SF
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Name _________________________
Pd _____
Chemistry
Mr. Harper
Sig Fig Practice
Measure the following lines with a ruler, record the length in cm, and determine the number of sig figs.
1.
Length: _________________
# of sig figs: ______________
Length: _________________
# of sig figs: ______________
Length: _________________
# of sig figs: ______________
2.
3.
Determine the number of sig figs in the following numbers.
4. _____1.37
14. _____142.00
5. _____378.42
15. _____0.0021
6. _____6.022
16. _____0.03987
7. _____8.470932
17. _____0.000670
8. _____270.
18. _____0.030900
9. _____6,542,000
19. _____5.00
10. _____100.
20. _____8 x 10-6
11. _____100
21. _____3.50 x 105
12. _____37.0
22. _____8200
13. _____37
23. _____8200
First, write down how many significant figures are in each number. Next, perform the calculation, writing down
the unrounded answer. Then, write the answer rounded to the correct number of significant figures:
1.
4.5 x 6.75
2.
3.0 / 2.3
3.
99.00 / 33
6
4.
70 x 3
5.
8.4 x 310
6.
0.43 x 1.69
7.
200 x 1.47
8.
3.940 / 3.70
9.
3.78 x 6.8
10.
8.51 / 30.10
11.
0.4080 x 1690
12.
200. x 0.071
13.
1000 x 3.000
14.
(5.20 x 0.67) / 4.100
15.
110 + 63
16.
92 + 75
17.
1.45 – 0.566
18.
3000 – 800
Measure the following rectangle with a ruler, record the length and width in cm, and determine the number of
sig figs. Then, calculate the area rounding the answer to the correct number of sig figs.
Length: _________________
# of sig figs: ______________
Width: _________________
# of sig figs: ______________
Area: __________________
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Name _________________________
Pd _____
Chemistry
Mr. Harper
Measurement Practice
Wooden Block
1. Measure the length, width, height of the wooden block to the smallest division of the ruler.
a. Length = ___________ cm
b. Width = ____________ cm
c. Height = ____________ cm
# of sig figs: __________
# of sig figs: __________
# of sig figs: __________
2. Calculate the volume in cubic centimeters and round to the correct number of sig figs.
a. Volume = length x width x height = ________________cm3
3. Measure the mass on the triple beam balance to the smallest division.
a. Mass = ______________ g
# of sig figs: ___________
4. Calculate the density in g/cm3 and round to the correct number of sig figs.
a. Density = mass / volume = __________________ g/cm3
Cylinder
5. Measure the diameter and height of the cylinder to the smallest division and calculate the radius.
a. Diameter = __________ cm
b. Height = ____________ cm
c. Radius = ____________ cm
# of sig figs: ___________
# of sig figs: ___________
# of sig figs: ___________
6. Calculate the volume in cm3 and round to the correct number of sig figs.
a. Volume = 3.14 x (radius)2 x height = ________________ cm3
7. Verify the volume measurement using the graduated cylinder. Volume = ______________ mL
8. Measure the mass in grams to the smallest division.
a. Mass = ______________ g
# of sig figs: ___________
9. Calculate the density in grams / cubic centimeter and round to the correct number of sig figs.
a. Density = mass / volume = ____________________ g/cm3
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Name ________________________
Chemistry
Mr. Harper
Scientific Notation Practice
Write the following numbers in scientific notation.
1) 61,050
_________________________
2) 0.0000809
_________________________
3) 90,100,000
_________________________
4) 300,000
_________________________
5) 0.075
_________________________
6) 0.000365
_________________________
7) 340,000,000
_________________________
8) 670
_________________________
9) 0.251
_________________________
10) 0.000000047
_________________________
Write the following numbers in long form.
11) 2.089 x 10-4
_________________________
12) 3.301 x 105
_________________________
13) 6 x 102
_________________________
14) 5.990 x 10-3
_________________________
15) 4.42 x 107
_________________________
16) 1.09 x 104
_________________________
17) 3.5 x 10-5
_________________________
18) 7.6 x 10-2
_________________________
19) 5.990 x 106
_________________________
20) 9.2 x 10-1
_________________________
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Perform the following calculations using your calculator. Write the answer in proper scientific notation.
21) (3 x 10 –6)(2 x 10-6)
22) (4 x 10-2)(1.5 x 109)
23) (8.0 x 103) / (4.0 x 10-7)
24) (3.0 x 104) / (2.00 x 105)
25) (6.0 x 105)(2.0 x 103)
26) (2.0 x 104)(4.00 x 10-8)
27) (5.0 x 103) / (8.0 x 106)
28) (2.00 x 10-4)2
29) (7.5 x 10-3)(2 x 106) / (3.0 x 10-4)
30) (5.00 x 10-3)3
31) (4.83 x 10-5) / (9.2 x 10-7)
32) (8.89 x 106)(4 x 10-3)
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