Scientific Notation
Period:
Chemistry
Name:
Date:
For all of these problems, when expressing numbers in scientific notation, do NOT write the ‘E’ as shown
on your calculator, write what it actually means  if your calculator shows 1.250E-4 that means 1.250x10-4.
1)
What is/are the rule(s) for the base number in scientific notation (in 2.54x1013, the base is the 2.54)?
1 ≤ mag. of base < 10
2)
What is/are the rule(s) for the exponent portion of scientific notation (everything after the x)?
 There must be a power of 10
 Exponent must be an integer
3)
For each of the following, the number as listed is not in correct scientific notation. Briefly state
what’s wrong with the number.
a. -25.42x10-4
b. 7.2x610
c. 5.4x103.2
d. 0.365x100
e. 10.2x10-5
mag. of base must be less than 10, but 25.42>10
must have a power of 10, not 6
exponent must be an integer, but 3.2 is not
mag. of base must be ≥ 1, but 0.365<1
mag. of base must be less than 10, but 10.2>10
there is no exponent shown
4)
f. 1.052x10
When you see a positive exponent in scientific notation, like 2.5x104, what does that really mean,
NOT the memory trick of moving the decimal?
Multiply by 10 as many times as the exponent,
representing a larger number than base
5)
When you see a negative exponent in scientific notation, like 2.5x10-4, what does that really mean,
NOT the memory trick of moving the decimal?
Divide by 10 as many times as the magnitude of the
exponent, representing a smaller number than base
For 6 – 11, convert the following expanded numbers into scientific notation
6) 792,600,000
7) -4,050,000
8) 0.000000233
7.92x108
-4.05x106
2.33x10-7
-4.5x10-7
0
10) 5.32 5.32x10
11) 0.00401
4.01x10-3
9) -0.00000045
For 12 – 17, expand the scientific notation to standard numerals.
12) 9.5 x 10-4
0.00095
15) -8 x 10-6
-0.000008
13) 8.98 x 107
89,800,000
16) 2.574 x 101
25.74
14) -4 x 105
-400,000
17) -1.02 x 100
-1.02
18) rank each of the following values from lowest to highest (1 being the lowest and 11 being highest),
then match the object that the number could be displaying to the value displayed:
the red numbers take the +/- into
account in the ranking, the blue numbers are the rank considering
only the magnitude of the numbers.
Note for rank, I’ll accept 2 versions as correct,
Rank:
9; 9
6; 4
5; 3
2; 5
10; 10
4; 2
3; 1
8; 8
7; 7
11; 11
1; 6
Values
Letter:
D
5.2x10 m G
2.1x10 m F
-8.6x10 m C
4.01x10 m J
9.12x10 m B
1.26x10 m K
4.22x10 m I
1.45x10 m H
1.496x10 m E
-1.103x10 m A
8.04x106 m
Measurement Description
a. altitude of the Marianas Trench relative to sea-level (about 6.8 mi
below sea-level)
0
b. width of a human hair
-2
c. altitude of Death Valley relative to sea-level (about 282 ft below
sea-level)
1
d. distance from Seattle to Paris as the crow flies (almost 5,000 mi)
7
e. distance from the Sun to the Earth (about 93 million miles)
-5
f. width of an adult’s finger
-10
g. length of a car
4
h. distance from B.I. to Seattle (about 9 mi)
4
i. length of a marathon
11
j. circumference of the Earth (almost 25,000 miles)
4
k. how far the protons are from the outer electrons, relative to the
upper surface, of an iron plate