4.8 Scientific Notation
Why use scientific notation??
When working with very large (astronomical!)
numbers or very small (microscopic!) numbers, it is
easier to write the numbers in scientific notation.
Ex.
We can estimate the number of stars in the Milky Way galaxy as
roughly 100 billion (100,000,000,000)
The diameter of a hydrogen atom is 0.00000000024 m
We can estimate the number of stars in the Milky Way galaxy as
roughly 100 billion (100,000,000,000)
The diameter of a hydrogen atom is 0.00000000024 m
It is MUCH easier to write these numbers using scientific
notation. There are two parts to scientific notation…
1. The number (which MUST be greater than or equal to 1 and
less than 10)
2. The number 10 with an exponent
A positive exponent indicates a large number.
A negative exponent indicates a small number.
We can estimate the number of stars in the Milky Way galaxy as
roughly 100 billion (100,000,000,000)
To write 100,000,000,000 in scientific notation, “move the
decimal point” so that the number part is between 1 and 10,
count as you move…
100,000,000,000
11 10
9 8 7
6 5 4
3 2 1
In scientific notation….
1.0 * 1011
The diameter of a hydrogen atom is 0.00000000024 m
To write 0.00000000024 in scientific notation, “move the
decimal point” so that the number part is between 1 and 10,
count as you move…
0.00000000024
1
2
3 4 5 6
7 8
9 10
In scientific notation….
2.4 * 10-10
Examples:
STANDARD FORM
300
3000
3250
32,500,000
0.03
0.0003
0.0000000325
0.00000000032
SCIENTIFIC NOTATION
3.0 × 102
3.0 × 103
3.25 × 103
3.25 × 107
3.0 × 10-2
3.0 × 10-4
3.25 × 10-8
3.2 × 10-10
SCIENTIFIC NOTATION
STANDARD FORM
2
3.0
×
10
300
3
3.0
×
10
3000
3
3.25
×
10
3250
7
3.25
×
10
32,500,000
3.0 × 10-2
0.03
3.0 × 10-4
0.0003
0.0000000325
3.25 × 10-8
0.00000000032
3.2 × 10-10
10 raised
to an
exponent
Number between 1 and 10
When writing a number in scientific notation there are 2 parts:
1. The number (which MUST be greater than or equal to 1 and
less than 10)
2. The number 10 with an exponent
A positive exponent indicates a large number.
A negative exponent indicates a small number.
Now try some:
EXERCISES: Express in scientific notation.
1. 450 = ___________________
2. 7500 = ___________________
3. 12,000,000 = ___________________
4. 720,000,000,000 = ___________________
5. 0.00325 = ___________________
6. 0.000000246 = ___________________
7. 0.00000000325 = _______________
8. 0.00000000436 = _________________
9. 480,000,000 = __________________
10. 93,200,000,000 = ________________
Now try some:
EXERCISES: Express in standard notation.
1) 2 x 103 = ___________________
2) 2.331 x 105 = ___________________
3) 9.51 x 1012 = ___________________
4) 5 x 10-3 = ___________________
5) 7.6278 x 10-5 = ___________________
6) 2.12 x 10-2 = ___________________
7) 3.14 x 10-4 = ___________________
8) 5.213 x 103 = ___________________
9) 7.49 x 104 = ___________________
10) 9.2 x 102 = ___________________