Significant figures Rules and Practice

Why do we care about significant figures? Where are you?

How to read equipment (number-line) for significant figures 1. Write down the numbers we are “sure of” meaning as exact as the lines and numbers on the equipment can go. Example: The graduated cylinder shows that you have between 25ml and 26ml of liquid. You write down 25. 2. Go one number further. Look at the lines and spacing and guess. It is okay if you are a little off. Example: It looks only slightly closer to the 25ml than the 26ml mark so you write down 25.4 ml

Practice Do the practice problems on the board

Accuracy, Precision, and Exactness Accuracy: how close a measurement is to “true” value. Precision - the repeatability of a measurement Exactness: making measurements to the correct level of uncertainty or significant figures

What is a significant figure It is the numbers in a measurement that can be counted on to be exact.

Rules for Sig. Fig.s Non-zero numbers are always significant Any zeros between two significant numbers are significant Any trailing zeros after the decimal point are significant. Exception: Exact numbers: If the statement is 100% true and always true. All numbers count as SF. Examples: 12in = 1 ft 24 hrs = 1 day

Practice How many significant figures are in each number 3500 501 0.020 800000 50000001

Practice How many significant figures are in each number 0.0000500 8.260 x 102 9000.01 501000 900000000.0

Rounding to a certain number of Significant figures Sometimes when doing a math problem you get a calculator answer with more numbers than you have significant figures. In that case you need to round. For example: Round 436.76 to 4 significant figures (so you want to keep the first 3 sig figs and round the 4th whichever direction is correct. #1-4 keep the same #, #5-9 round up) At the end check by counting the # of Sig Figs and checking the digits are in the right places.

Rounding Practice Round 1235 to 2 significant figures

Class/Home work Read chapter 2.5 Answer Questions and Problems (located at the end of the chapter, pg 47): #37-39, 43

Adding and Subtracting Significant Figures Steps: Change all measurements to the same unit/exponent before adding or subtracting. Put the numbers in the calculator and get the answer. Round the answer to the decimal place of the original number with least exact place (tenths, hundredths, etc.)

Adding/Subtracting Practice 1 + 1.5 55 + 9.432 432 – 20 0.0043 + 0.011 4008 - 550

Adding/Subtracting Practice 543.234 + 7652.21 + 32.4 88000 – 5377 - 63300.0 0.002345 + 0.0424 – 0.0010000 500000.0 + 328 – 0.9932 7.345 + 432.0 – 30

Class/Home work If you need help, we are still in chapter 2.5 Answer: #46, 49-51, 52abc Note: 52d is harder than I expect you to be able to do at this point. Give it a try if you want.

Rules for Multiplying and Dividing Put it in the calculator and get the answer. Count the number of significant figures for the original numbers. Round the answer’s significant figures to the same amount as the original number with the least significant figures.

Practice 23 x 0.043 3.05 / 0.00045210 0.00020402 x 800000 320 / 0.004210 x 0.0093 45300001 x 0.0004320 / 0.00235

Rules for multiplying / dividing with exponents (scientific notation) Multiply/divide any numbers in front of the 10x. When multiplying exponents, add them together When dividing exponents subtract. Write answer with correct significant figures.

Practice 1 x 103 x 4 x 104 0.045 x 10-6 / 5.01 x 106 5030 x 1035 x 3.4 x 10-27 / 0.4 x 104

Homework Chapter 2: 47, 48, 53, 54 (with answers)