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In science, we deal with some very LARGE numbers: 1 mole = 602000000000000000000000 In science, we...
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Transcript of In science, we deal with some very LARGE numbers: 1 mole = 602000000000000000000000 In science, we...
In science, we deal with some In science, we deal with some very very LARGELARGE numbers: numbers:
1 mole = 6020000000000000000000001 mole = 602000000000000000000000
In science, we deal with some In science, we deal with some very very SMALLSMALL numbers: numbers:
Mass of an electron =Mass of an electron =0.000000000000000000000000000000091 kg0.000000000000000000000000000000091 kg
Scientific NotationScientific Notation
Imagine the difficulty of Imagine the difficulty of calculating the mass of 1 mole calculating the mass of 1 mole of electrons!of electrons!
0.00000000000000000000000000000000.000000000000000000000000000000091 kg91 kg x 602000000000000000000000x 602000000000000000000000
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Scientific Scientific Notation:Notation:A method of representing very large A method of representing very large or very small numbers in the form:or very small numbers in the form:
M x 10M x 10nn
MM is a number between is a number between 11 and and 1010 nn is an integer is an integer
2 500 000 000
Step #1: Insert an understood decimal pointStep #1: Insert an understood decimal point
.
Step #2: Decide where the decimal Step #2: Decide where the decimal must end must end up so that one number is to its up so that one number is to its leftleftStep #3: Count how many places you Step #3: Count how many places you bounce bounce the decimal pointthe decimal point
123456789
Step #4: Re-write in the form M x 10Step #4: Re-write in the form M x 10nn
2.5 x 102.5 x 1099
The exponent is the number of places we moved the decimal.
0.00005790.0000579
Step #2: Decide where the decimal Step #2: Decide where the decimal must end must end up so that one number is to its up so that one number is to its leftleftStep #3: Count how many places you Step #3: Count how many places you bounce bounce the decimal pointthe decimal pointStep #4: Re-write in the form M x 10Step #4: Re-write in the form M x 10nn
1 2 3 4 5
5.79 x 105.79 x 10-5-5
The exponent is negative because the number we started with was less than 1.
Multiplication and DivisionMultiplication and Division
m
n
10
10= mn10
10n
10m= 10n-m
10n × 10m = 10m+n
(10m)n = 10 m ×n
Practice ProblemsPractice Problems
158000 m
1.58* 105m
0.000009782 9.782* 10-6
837100000 8.371 * 108
12552000 1.2552 * 107
0.0054 5.4 * 10-3
3,200,000 3.2 * 106