UNDERSTANDING SIGNIFICANT FIGURES. Towson University Academic Achievement Center CK524

Transcription

1 UNDERSTANDING SIGNIFICANT FIGURES Towson University Academic Achievement Center CK524

2 HOW MANY SIG FIGS ARE IN A NUMBER? We re going to use a map of the United States to help us. First question to ask ourselves, is if a decimal is present or not.

3 If it s Present, start counting at the first non-zero from the Pacific side and keep counting until the end. If it s Absent, start counting at the first non-zero number from the Atlantic side and keep counting until the end.

4 YOUR TURN!!!

5 NOW, LET S DO SOME ADDITION (OR SUBTRACTION) 1. Count up the decimal places in every number 2. Identify the number with the least amount of decimal places 3. Solve the problem as normal with all decimal places 4. Round your number to the same number of decimal places as the number in step 2

6 AN EXAMPLE =? Count up the decimal places in every number Identify the number with the least amount of decimal places 3. Solve the problem as normal with all decimal places 4. Round your number to the same number of decimal places as the number in step 2

7 YOUR TURN!!! X10^23-3.3X10^16

8 LET S APPLY THIS TO LAB Suppose that a mixture of 8g of sugar, 52.0 g of salt, and g of flour is prepared. What is the total mass of the mixture expressed in exponential notion and with proper significant figures? 1.13 x 10 2

9 ALL RIGHT.TIME TO MOVE ON TO MULTIPLICATION AND DIVISION 1. Count up the sig figs in every number 2. Identify the number with the least amount of sig figs 3. Solve the problem as normal with all sig figs 4. Round your number to the same number of sig figs as the number in step 2

10 BIG PICTURE!!! Addition/Subtraction Use Decimals Multiplication/Division Use Sig Figs

11 AN EXAMPLE 23 x =? Count up the sig figs in every number 2. Identify the number with the least amount of sig figs 3. Solve the problem as normal with all decimal places 4. Round your number to the same number of sig figs as the number in step 2

12 YOUR TURN!!! X X 62.0 / X 10^13 / 3.3 X 10^16

13 LET S APPLY THIS TO LAB Suppose there are 412 Quercus alba (white oak trees) and 5563 Rhododendron arborescens (sweet azalea bushes) in 5.2 acres at a state park. How many individuals of each species are in one acre? 79 white oaks 7.9 x 10 1 white oaks 1100 sweet azalea 1.1 x 10 3 sweet azaleas

14 ANOTHER LAB APPLICATION.. A thermometer in lab reads 52.3 C. You are curious what that is in F. Use the below equation to convert C to F: C x 9/ = F 126 Important Note!!! Constants (such as 9/5, 9.81, etc.) do not Count when determining sig figs!!!

15 OTHER WEIRD THINGS YOU MIGHT ENCOUNTER So we already know that constants don t count for sig figs, but what about other things? Exact values i.e.) 7 apples, 12 eggs in one dozen DO NOT count Inexact values i.e.) π, c =3.00 m/s, anything you measure DO count

16 OTHER WEIRD THINGS YOU MIGHT ENCOUNTER Trig functions follow the same rules for sig figs as multiplication and division Exponents do not count for sig figs, only the number raised to the exponent i.e.) has 3 sig figs Lab application: number derived from graphs i.e.) slope or y intercept only have as many significant figures as the data point with the least amount of significant figures ALWAYS ASK YOUR PROFESSOR IF YOU RE UNSURE!

17 ADDITION, SUBTRACTION, 3.Move onto the next group and use the sig fig rules for that group and the number you got from step 2 MULTIPLICATION, AND DIVISION. OH MY! 1.Use the order of operations to determine what group of numbers to start with (PEMDAS) 2.While working within one group ie) P, or MD, do not round with appropriate sig figs until you ve finished with that one group

18 AN EXAMPLE ( ) =? (-5.2) =? (-.82) = Use the order of operations to determine what group of numbers to start with (PEMDAS) 2. While working within one group ie) P, or MD, do not round with appropriate sig figs until you ve finished with that one group 3. Move onto the next group and use the sig fig rules for that group and the number you got from step 2 4. Repeat this process for each group until the end

19 YOUR TURN!!! 3.6^6 x (1.25 x 10^ x 10^2 (TAN(43) )^2 +.5 ( ) x COS(35) ^3

20 MORE LAB APPLICATION When using digital equipment, always record the exact number that comes from the machine (including ALL zeros) When doing measurements yourself, always estimate to one more significant digit than what is shown.

21 MORE LAB APPLICATION

22 MORE PRACTICE

23 Made for Towson University s Academic Achievement Center 2013 Contact us for more information! achieve@towson.edu