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Significant Figures & Scientific Notation Practice Problems!
Counting Significant Figures: RULES For Counting Sig. Figs:
1) Nonzero integers- (1-9) Always count as significant figures.
2) Zeros-There are three classes of Zeros.
a. Leading Zeros are zeros that precede all of the nonzero digits. They never count as
Sig Figs.
b. Captive Zeros- are zeros that fall between nonzero digits. They always count as Sig
Figs.
c. Trailing Zeros- are zeros at the right end of the number. They are significant only if
the number is written with a decimal point.
1) 7000
2) 450.0
3) 350
4) 44 578
5) 305
6) 0.006200
7) 565.05
8) 5500
9) 74.00
10) 7040.0
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
23.7 x 10-2
1.4 x 107
4.293 x 104
705
600
4301.0
0.00056
40280
33214
2.003
Adding & Subtracting Sig Figs:
RULE: When adding or subtracting your answer can only show as many decimal places as the
measurement having the fewest number of decimal places.
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 =
7) 357.89 + 0.002 =
8) 17.95 + 32.42 + 50 =
9) 5.5 + 3.7 + 2.97 =
10) 84.675 - 3 =
11) 75 - 2.55 =
12) 10 - 9.9 =
Multiplying & Dividing Sig Figs:
RULE: When multiplying or dividing, your answer may only show as many significant digits as the
multiplied or divided measurement showing the least number of significant digits.
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 =
7) 3.14 x 5.6=
8) 300 x 10.6=
9) 0.059 x 6.95=
10) 80/0.675=
11) 0.003/106=
12) 8.5/0.356=
Scientific Notation:
Part I. Change the following numbers to proper
scientific notation
1) 65.7
2) 0.00545
3) 22 450 000
4) 0.0803
5) 678.3
6) 3 450 000
7) 0.0803
8) 678.3
9) 3 450 000
10) 602,200,000,000,000,000,000,000
Part II. Change the following numbers to
standard notation
8.85 x 104
1.847 x 102
3.400 x 10-3
6.5 x 10-2
9.7 x 102
1.4 x 10-1
6.5 x 10-2
9.7 x 108
1.4 x 10-1
10. 6.022 x 1023
1.
2.
3.
4.
5.
6.
7.
8.
9.
Multiplication & Division with Scientific Notation:
Rules for Multiplication- When you multiply numbers with scientific notation, multiply the coefficients
together and add the exponents. The base will remain 10.
Rules for Division: When dividing with scientific notation, divide the coefficients and subtract the
exponents. The base will remain 10
1) (6.8 x 103) x (4.54 x 106)
2) (2.0 x 10-1) x (8.5 x 105)
3) (4.42 x 10-3) x (4 x 10-2)
4) divide (3 x 106) by (7 x 10-7)
5) divide (9.2 x 10-3) by (6.3 x 106)
6) divide (2.4 x 106) by (5.49 x 10-9)
7) (2.87 x 105) x (3.514 x 109)
8) (5.0 x 10-2) x (7.85 x 104)
9) (1.042 x 10-1) x (4.002 x 10-5)
10) divide (2.21 x 105) by (1.807 x 10-7)
11) divide (1.92 x 10-2) by (2.3 x 106)
12) divide (9.4 x 102) by (1.24 x 10-5)
Percent Error Calculations:
(Observed Value - True Value)
Percent Error = -------------------------------------------------- x 100%
True Value
1. Working in the laboratory, a student find the density of a piece of pure aluminum to be 2.85 g/cm3.
The accepted value for the density of aluminum is 2.699 g/cm3. What is the student's percent error?
2. A student experimentally determines the specific heat of water to be 4.29 J/g x Co. He then looks up
the specific heat of water on a reference table and finds that is is 4.18 J/g x Co. What is his percent
error?
3. A student takes an object with an accepted mass of 200.00 grams and masses it on his own balance.
He records the mass of the object as 196.5 g. What is his percent error?