Why is this stuff important? Figure: 02-03UN20 Title: Converting concentration to mass Caption: A patient requires an injection of 0.012 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

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

Form: (# from 1 to 9.999) x 10exponent 800 = 8 x 10 x 10 = 8 x 102 2531 = 2.531 x 10 x 10 x 10 = 2.531 x 103 0.0014 = 1.4 / 10 / 10 / 10 = 1.4 x 10-3

Change to standard form. 1.87 x 10–5 = 3.7 x 108 = 7.88 x 101 = 2.164 x 10–2 = 000000187000000 . . 0.0000187 370,000,000 78.8 0.02164

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

Using the Exponent Key on a Calculator 2nd EE EXP

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

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

Example: 1.2 x 105 2.8 x 1013 = 1 . 2 EE 5 3 8 Type this calculation in like this: 2nd 2nd 4.2857143 –09 Calculator gives… 4.2857143 E–09 or… This is NOT written… 4.3–9 4.3 x 10–9 4.3 E –9 or But instead is written…

(–) = -6.525 x 10-9 report -6.5 x 10-9 (2 sig. figs.) = 5.3505 x 103 or 5350.5 report 5.35 x 103 (3 sig. figs.) = 5.84178499 x 10-13 report 5.84 x 10-13 (3 sig. figs.) = 2.904 x 1023 report 2.9 x 1023 (2 sig. figs.) = -3.07122 x 1016 report -3.1 x 1016 (2 sig. figs.)

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

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 10-7 by 3.1 x 1014 7.74 x 10-22

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 ) + ( 2.16 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

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 1.240560 x 106 mg 6 x 104 sec 246.31 g 20.06 cm 1.050 m 2 7 1 5 4 0.12 kg 1240560. cm 6000000 kg 6.00 x 106 kg 409 cm 29.200 cm 0.02500 g 2 7 1 3 5 4