Study Guide Test: Unit 1D
Significant Figures, Rounding, & Scientific Notation
What you need to know:
1)
2)
3)
4)
5)
6)
Be able to determine significant figures in a given number.
Be able to apply the rules for rounding numbers.
Be able to apply the rules for significant figures in addition/subtraction and multiplication/division problems.
Be able to convert numbers from decimals to scientific notation and back again.
Be able to perform all calculations using scientific notation.
Bonus Questions: Conversion Factors, Area, Volume, Density, & % Error
There is a wealth of self-help information under the “On-Line Tutoring” link on the Home Page!
1) Significant figures in a given number.
The bold ones count
a) In a number less than 1, leading zeroes, in front of non-zero numbers, never count. They are only
placeholders
b) Non-zero digits always count. 1,2,3,4,5,6,7,8,9
c) Zeroes between non-zero digits always count. 3008
d) Zeroes at the end of decimal digits always count. 000.003000
e) Zeroes in a whole number only count if there’s a decimal after them. 5600.
Practice: Determine the number of significant figures in the examples below
1)
5)
9)
13)
17)
6.570 = 4
0.00157 = 3
30.079 = 5
440.0006 = 7
504.52 = 5
2)
6)
10)
14)
18)
000.12090 = 5
1002.6090 = 8
43.07 = 4
0.00000002 = 1
0.0230 = 3
3)
7)
11)
15)
19)
26.509 = 5
28.0 = 3
0.305060 = 6
23000 = 2
.000302 = 3
4)
8)
12)
16)
20)
0.070456 = 5
1071 = 4
000.000228 = 3
6800.000 = 7
10.00500 = 7
2) Rounding numbers.
a) If the number following the number you want to round is 6 or greater round up.
b) If the number following the number you want to round is 4 or less do not round up.
c) If the number following the number you want to round is 5 and there is any number following the 5 round
up.
d) If the number following the number you want to round is 5 with no number following it fall back on the
“odd even rule”.
i. Do not round up even numbers, (0 is even).
ii. Round up odd numbers.
Practice: Round the numbers below to 3 significant figures. Put them into Correct Scientific Notation 1st if
needed
1)
5)
9)
13)
17)
6.070 = 6.07
3.00157 = 3.00
30.0235 = 3.00x101
440.078006 = 4.40x102
504.52 = 5.05x102
2)
6)
10)
14)
18)
9000.12090 = 9.00x103
13000 = 1.30x104
08973.7 = 8.97x104
0557.002 = 5.57x102
70.0230 = 7.00x101
3)
7)
11)
15)
19)
66.509 = 6.65x101
28.000 = 2.80x101
0.307860 = 3.08x10-1
23044 = 2.30x104
.089902 = 8.99x10-2
4)
8)
12)
16)
20)
0.055056 = 5.51x10-2
10710.33 = 1.07x104
0.000228 = 2.28x10-4
688.445 = 6.88x102
10507 = 1.05x104
3)
Examples: Significant figures in add/sub & mult/div problems.
How many significant figures you keep in your answer depends on whether the problem is
addition/subtraction or multiplication/division.
a) Addition / Subtraction: Your answer can only have as many numbers, including zero, on the right side
of the decimal point as the number in the problem with the least numbers to the right of the decimal point.
b) Multiplication / Division: Your answer can only have as many significant figures as the number in the
problem with the least amount of significant figures.
Convert ALL answers into correct scientific notation BEFORE rounding
Addition Practice: Express your answer using the appropriate number of significant figures
1)
6.563 + 8.0 + 4.37 = 1.9x101
2)
80.0853 + 0.047 + 0.07 + 0.7 = 8.1x101
3)
3.25 + 10.00 + 9.66 = 2.29x101
4)
525.37 + 6.50 + 15.07 + 58.56 = 6.06x102
Subtraction Practice: Express your answer using the appropriate number of significant figures
1)
323.27 - 172.8 = 1.5x102
2)
97.032 - 1976.2 - 9.002 = 1.9x103
3)
103.57 - 6.53 = 9.70x101
4)
5.037 - 335.07 - 18.60 = 3.49x102
Multiplication Practice: Express your answer using the appropriate number of significant figures
1)
976.5 x 4.37 = 4.27x103
2)
10.0853 x .0387 = 3.90x10-1
3)
13.25 x 10.00 x 9.6 = 1.3x103
4)
895.37 x 6.850 = 6.133x103
Division Practice: Express your answer using the appropriate number of significant figures
1)
483.27 / 2.058 = 2.348x102
2)
690.032 / 8.002 = 8.623x101
3)
43.587 / 6.03 = 7.23
4)
92.37 / 175.07 = 5.276x10-1
4)
Scientific Notation:
Be able to express all answers in proper scientific notation
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The format for writing a number in scientific notation is fairly simple:
 Only one number can be to the left of the decimal point.
 The number to the left of the decimal point must be between 1 and 9. NO zeros!
 When the decimal point is moved to the left the exponent is made larger by the number of spaces
moved. Left = Larger Exponent
 When the decimal point is moved to the right the exponent is reduced by the number of spaces moved.
Right = Reduced Exponent.
Practice: Convert the Decimal Form into Scientific Notation:
1)
3)
5)
0.00006797 = 6.797x10-5
85400 = 8.54x104
88.0000069 = 8.80000069x101
2)
4)
6)
0.000003804 = 3.804x10-6
280.0000003 = 2.800000003x102
0.00455332 = 4.55332x10-3
Practice: Convert the Scientific Notation into Decimal Form:
1)
3)
5)
8.306 X 107 = 83060000
6.0605 X 10-5 = 0.000060605
8.0007 X 108 = 800070000
5)
Exponents in calculations using scientific notation.
2)
4)
6)
0086.09 X 10-12 = 0.00000000008609
4546.829703 X 102 = 454682.9703
882.5002 X 10-2 = 8.825002
ALL previous rules apply. Now there are a few rules about exponents that need to be followed
a) Addition/Subtraction Rule: Both Exponents must be the same.
* Follow the rules for significant figures in the answer of keeping the least numbers behind the decimal point
using the numbers in the problem AFTER you change them to have matching exponents.
b) Multiplication Rule: Add the exponents. They don’t have to be the same.
c) Division Rule: Subtract the bottom exponent, in the denominator, from the top exponent, in the
numerator.
Addition/Subtraction with Exponents Practice: Express your answer using the appropriate number of
significant figures
1)
(8.88 x 102) + (6.45 x 104) = 6.54x104
2)
(8.5 x 109) + (6.45 x 1010) = 7.30x1010
3)
(6.098 x 107) - (3.45 x 108) = -2.84x108
4)
(37.004 x 105) - (1.59 x 106) = 2.11x106
Multiplication with Exponents Practice: Express your answer using the appropriate number of significant
figures.
5)
(8.88 x 102)(6.45 x 10-10) = 5.73x10-7
6)
(8.5 x 109)(6.45 x 1010) = 5.5x1020
Division with Exponents Practice: Express your answer using the appropriate number of significant figures.
7)
4.44 x 107 / 2.25 x 105 = 1.80x105
6)
BONUS: Know how to perform the following calculations
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Area = L x W
Volume = L x W x H
8)
37.004 x 10-5 / 1.59 x 106 = 2.33x10-10
Calculate both using conversion factors for dimensions in different units.
a) Calculate the Area of an object with the following dimensions. Express your answer in cm2
L = .0893km, W = 3345cm
b) Calculate the Volume of an object with the following dimensions. Express your answer in cm3
L = .121dam, W = 205cm, H = 84786mm
Density: Density = M / V, Mass = D x V, Volume = M / D
% Error: Experimental Value – Accepted Value / Accepted Value x 100