Aim: Why are Significant Figures Important? Do Now: Read the ruler below. At what number is the pointer at. Be as accurate as possible.

Accuracy is how correct something is, or how close to the true value Accuracy vs Precision Accuracy Precision Accuracy is how correct something is, or how close to the true value Precision is how close your measurements are to each other, or how consistent something is

Accuracy vs. Precision Match the following: Low accuracy and High Precision Low accuracy and low precision High accuracy and high precision High Accuracy and low precision A. D. B. C.

Significant Figures All measurements are inaccurate due to: Precision of measuring device Human error Faulty technique

Let’s try graduated cylinders Look at the graduated cylinder below What can you read with confidence? 56 ml Now estimate the last digit 56.0 ml

One more graduated cylinder Look at the cylinder below… What is the measurement? 53.5 ml

Significant Figures Significant figures in a measurement include all of the digits that are known precisely plus one last digit that is estimated.

All non zero digits are ALWAYS significant How to determine how many significant figures a measurement has Rule #1 All non zero digits are ALWAYS significant How many significant digits are in the following numbers? 3 Significant Figures 5 SF 4 SF 274 25.632 8.987

Rule #2 All zeros between significant digits are ALWAYS significant How many significant digits are in the following numbers? 3 SF 5 SF 4 SF 504 60002 9.077

Rule #3 Zeros after non-zero digits are significant when a decimal is present. How many significant digits are in the following numbers? 32.0 19.000 105.0020 3 SF 5 SF 7 SF

Rule #4 All zeros that act as place holders are NOT significant Zeros before non-zero digits are not significant 0.0000000123 3 SF Zero after non-zero digit with no decimal are not significant 1000 1 SF

For example 1 SF 1) 0.0002 3 SF 2) 6.02 x 1023 6 SF 3)100.000 2 SF How many significant figures are in the following numbers? 1 SF 3 SF 6 SF 2 SF 1) 0.0002 2) 6.02 x 1023 3)100.000 4)150000 5) 800

Sig Fig Rounding Example: Round the following measured number to 4 sig figs: 82.56702

Sig Fig Rounding Example Round the following measured number to 4 sig figs: 82.56702

Sig Fig Rounding Example Round the following measured number to 4 sig figs: 82.56702 ANSWER: 82.57

Adding Significant Zeros Sometimes a calculated answer requires more significant digits. Then one or more zeros are added. Calculated Answer Zeros Added to Give 3 Significant Figures 4 4.00 1.5 1.50 0.2 0.200 12 12.0

Practice Rounding Numbers

Significant Figures Round each to 3 sig figs b) 0.000230600 c) 2568 d) 2562 e) 8

Significant Figures Round each to 3 sig figs a). 28.394 ANSWER: 28.4 b). 0.000230600 ANSWER: 0.000231 c). 2568 ANSWER: 2570 d). 2562 ANSWER: 2560 e). 8 ANSWER: 8.00

Addition and Subtraction When adding or subtracting, use The same number of decimal places in your final answer as the measurement with the fewest decimal places (least precise measurement). Use rounding rules to adjust the number of digits in the answer. 25.2 one decimal place + 1.34 two decimal places 26.54 calculated answer 26.5 answer with one decimal place

Multiplication and Division When multiplying or dividing, use The same number of significant figures in your final answer as the measurement with the fewest significant figures. Rounding rules to obtain the correct number of significant figures. Example: 110.5 x 0.048 = 5.304 = 5.3 (rounded) 4 SF 2 SF calculator 2 SF

Calculations

Scientific Notation Scientific Notation allows us to display massive and tiny numbers in a universal simple way. Instead of writing 4,000,000 we would write 4.0 x 106 All we are doing is moving the decimal to the right of the first non-zero number We then write x 10the number of places we moved the decimal On a BIG number, we move the decimal left and the exponent is positive On a LITTLE number, we move the decimal right and the exponent is negative

Converting to Scientific Notation Example: Write 5,000,000,000 in scientific notation 5 000 000 000 Now we write 5.0 x 109 because we moved the decimal 9 places to the left

Converting to Scientific Notation Example: Write 0.0005723 in scientific notation 0 . 0005723 Now we write 5.723 x 10-4 because we moved the decimal 4 places to the right

Scientific Notation Practice Practice writing these in Scientific Notation: Practice writing these in from Scientific Notation: 5) 8.2 x 102 6) 9.63 x 10-5 7) 7.22 x 105 8) 1.23456 x 10-4 300 420 0.34 0.00034

Scientific Notation and Calculators Different ways calculators express scientific notation

Scientific Notations and Calculations Whenever doing calculations on a calculator with scientific notation, ALWAYS put the scientific notation in parenthesis Ex: (1.23 x 104 ) / (5.67 x 10-8)

Calculations