1. Scientific Notation Often used to express very large or
very small numbers.
Also used to maintain
correct number of
significant figures.

2. Form: (# from 1 to 9.999) x 10exponent
800 = 8 x 10 x 10
= 8 x 102
2531 = x 10 x 10 x 10
= x 103
= 1.4 / 10 / 10 / 10
= 1.4 x 10-3

3. Change to standard form.
1.87 x 10–5 =
3.7 x 108 =
7.88 x 101 =
2.164 x 10–2 = . .
370,000,000
78.8

4. Change to scientific notation.
12,340 =
0.369 =
0.008 =
1,000,000,000 =
1.234 x 104
3.69 x 10–1
8 x 10–3
1 x 109

5. Using the Exponent Key on a Calculator

6. EE or EXP means “times 10 to the…”
How to type out 6.02 x 1023:
How to type out 6.02 x 1023: 6 EE . 3 2 6 EE . 3 2
Don’t do it like this…
WRONG! 6
y x . 3 2
WRONG!
…or like this… x 1 6 . 2 EE 3
…or like this:
TOO MUCH WORK.
y x 3 2 x 1 6 .

7. Also, know when to hit your (–) sign…
…before the number,
…after the number,
…or either one.

8. Example:
1.2 x 105
2.8 x 1013 = 1 . 2 EE 5 3 8
Type this calculation in like this:
–09
Calculator gives…
E–09
or…
This is NOT written…
4.3–9
4.3 x 10–9
4.3 E –9 or
But instead is written…

9. = x 10-9
report -6.5 x 10-9 (2 sig. figs.)
= x 103 or
report 5.35 x 103 (3 sig. figs.)
= x 10-13
report 5.84 x (3 sig. figs.)
= x 1023
report 2.9 x 1023 (2 sig. figs.)
= x 1016
report -3.1 x 1016 (2 sig. figs.)

10. Scientific Notation Scientific Notation
Converting Numbers to Scientific Notation
How to Use a Scientific Calculator

11. Scientific Notation
We often use very small and very large numbers in chemistry.
Scientific notation is a method to express these numbers in a
manageable fashion.
Thus cm can be written 1 x 10-7 cm.
Lets see why…
Scientific notation expresses a number as the product of two
factors, the first falling between 1 and 10 and
the second being a power of 10.

12. 6.02 x 1023 Method to express really big or small numbers.
Format is Mantissa x Base Power
Decimal part of
original number
Decimal
you moved
6.02 x 1023
We just move the decimal point around.

13. Scientific Notation 5000 = 5 x 103 or 5 3 EE 5 x (10 x 10 x 10)
Numbers are written in the form M x 10n, where the factor
M is a number greater than or equal to 1 but less than 10 and
n is a whole number.
= 5 x or
5 x (10 x 10 x 10)
5 x 1000
5000
Numbers > one have a positive exponent.
Numbers < one have a negative exponent.
x 10n EE

14. Converting Numbers to Scientific Notation
2.205 x 10-5 1 2 3 4 5
In scientific notation, a number is separated into two parts.
The first part is a number between 1 and 10.
The second part is a power of ten.

15. How to Use a Scientific Calculator
Divide: (5.44 x 107) (8.1 x 104) .
5.44
8.1 00 07 00 04
How to enter this on a calculator: . EE . EE
ENTER OR .
EXP .
EXP =
rounded to 6.7 x 102
Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 52

16. Rule for Multiplication Calculating with Numbers Written in Scientific Notation
When multiplying numbers in scientific notation, multiply the
first factors and add the exponents.
Sample Problem: Multiply 3.2 x by 2.1 x 105
(3.2) x (2.1) = 6.72
6.72 x 10-2
(-7) + (5) = -2 or 10-2
Exercise: Multiply 14.6 x 107 by 1.5 x 104
2.19 x 1012

17. Rule for Division Calculating with Numbers Written in Scientific Notation
When dividing numbers in scientific notation, divide the first
factor in the numerator by the first factor in the denominator.
Then subtract the exponent in the denominator from the
exponent in the numerator.
Sample Problem: Divide 6.4 x 106 by x 102 .
(6.4) (1.7) = 3.76 .
3.76 x 104
(6) - (2) = 4 or 104
Exercise: Divide 2.4 x by 3.1 x 1014
7.74 x 10-22

18. Rule for Addition and Subtraction Calculating with Numbers Written in Scientific Notation
In order to add or subtract numbers written in scientific
notation, you must express them with the same power of 10.
Sample Problem: Add 5.8 x 103 and x 104
(5.8 x 103) + (21.6 x 103) =
27.4 x 103
2.74 x 104
Exercise: Add 8.32 x and 1.2 x 10-5
1.28 x 10-5

19. Using Scientific Notation for Expressing the Correct Number of Significant Figures
Measurement Number of significant
figures it contains
Measurement Number of significant figures it contains
25 g
0.030 kg
x 106 mg
6 x 104 sec g
20.06 cm
1.050 m 2 7 1 5 4
0.12 kg cm kg
6.00 x 106 kg
409 cm cm g 2 7 1 3 5 4

20. Scientific Notation Scientific Notation Scientific Notation Keys