1. Why is this stuff important? Figure: 02-03UN20 Title:
Converting concentration to mass
Caption:
A patient requires an injection of g of a painkiller available as a 15 mg/mL solution. How many milliliters should be administered?
Notes:
Knowing the amount of painkiller in 1 mL allows us to use the concentration as a conversion factor to determine the volume of solution that would contain the desired amount.
Keywords:
calculations, conversions

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

3. 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

4. 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

5. 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

6. Using the Exponent Key on a Calculator
2nd EE
EXP

7. 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

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

9. Example:
1.2 x 105
2.8 x 1013 = 1 . 2 EE 5 3 8
Type this calculation in like this:
2nd
2nd
–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…

10. (–)
= 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.)

11. 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 10-7 )x (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 ) X (1.5 x 104 )
2.19 x 1012

12. 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 (1.7 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

13. 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 ) + ( x 104 )
(5.8 x 103) + (21.6 x 103) =
27.4 x 103
2.74 x 104
Exercise: Add (8.32 x 10-7 ) + (1.2 x 10-5 )
1.28 x 10-5

14. 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