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Solving Problems: A Chemistry Handbook
Chemistry: Matter and Change
11
SOLVING PROBLEMS:
A CHEMISTRY HANDBOOK
CHAPTER
2
2.2 Scientific Notation and Dimensional Analysis
Extremely small and extremely large numbers can be compared
more easily when they are converted into a form called scientific
notation. Scientific notation expresses numbers as a multiple of two
factors: a number between 1 and 10; and ten raised to a power, or
exponent. The exponent tells you how many times the first factor
must be multiplied by ten. When numbers larger than 1 are
expressed in scientific notation, the power of ten is positive. When
numbers smaller than 1 are expressed in scientific notation, the
power of ten is negative. For example, 2000 is written as 2 ϫ 10 3 in
scientific notation, and 0.002 is written as 2 ϫ 10 Ϫ3 .
Example Problem 2-4
Expressing Quantities in Scientific Notation
The surface area of the Pacific Ocean is 166,000,000,000,000 m 2 .
Write this quantity in scientific notation.
To write the quantity in scientific notation, move the decimal point
to after the first digit to produce a factor that is between 1 and 10.
Then count the number of places you moved the decimal point; this
number is the exponent (n). Delete the extra zeros at the end of the
first factor, and multiply the result by 10 n . When the decimal point
moves to the left, n is positive. When the decimal point moves to the
right, n is negative. In this problem, the decimal point moves
14 places to the left; thus, the quantity is written as 1.66 ϫ 10 14 in
scientific notation.
Practice Problems
13. Express the following quantities in scientific notation.
a. 50,000 m/s 2
b. 0.00000000062 kg
c. 0.000023 s
d. 21,300,000 mL
e. 990,900,000 m/s
f. 0.000000004 L
Solving Problems: A Chemistry Handbook
Chemistry: Matter and Change
11
SOLVING PROBLEMS:
A CHEMISTRY HANDBOOK
CHAPTER
2
2.2 Scientific Notation and Dimensional Analysis
Extremely small and extremely large numbers can be compared
more easily when they are converted into a form called scientific
notation. Scientific notation expresses numbers as a multiple of two
factors: a number between 1 and 10; and ten raised to a power, or
exponent. The exponent tells you how many times the first factor
must be multiplied by ten. When numbers larger than 1 are
expressed in scientific notation, the power of ten is positive. When
numbers smaller than 1 are expressed in scientific notation, the
power of ten is negative. For example, 2000 is written as 2 ϫ 10 3 in
scientific notation, and 0.002 is written as 2 ϫ 10 Ϫ3 .
Example Problem 2-4
Expressing Quantities in Scientific Notation
The surface area of the Pacific Ocean is 166,000,000,000,000 m 2 .
Write this quantity in scientific notation.
To write the quantity in scientific notation, move the decimal point
to after the first digit to produce a factor that is between 1 and 10.
Then count the number of places you moved the decimal point; this
number is the exponent (n). Delete the extra zeros at the end of the
first factor, and multiply the result by 10 n . When the decimal point
moves to the left, n is positive. When the decimal point moves to the
right, n is negative. In this problem, the decimal point moves
14 places to the left; thus, the quantity is written as 1.66 ϫ 10 14 in
scientific notation.
Practice Problems
13. Express the following quantities in scientific notation.
a. 50,000 m/s 2
b. 0.00000000062 kg
c. 0.000023 s
d. 21,300,000 mL
e. 990,900,000 m/s
f. 0.000000004 L