Accuracy Precision Using Significant Figures S 8 CS

Accuracy & Precision: Using Significant Figures S 8 CS 3: Students will have the computation and estimation skills necessary for analyzing data and following scientific explanations. S 8 CS 3 d: Decide what degree of precision is adequate, and round off appropriately. S 8 CS 3 e. : Address the relationship between accuracy and precision.

Measurements in Science Accuracy and precision are both important to have in any science experiment. � Accuracy is how close a measured value is to the actual (true) value. � Precision refers to reliability and is how close the measured values are to each other. It includes the number of significant digits to which a value has been reliably measured

It’s Friday! � 1. Initial roster � 2. Pick –up hand outs next to roster � 3. Put your name on all 3 � 4. Warm-up: � Complete the ws with the snake (snake side only)

Precise(precision) � Repeatable � Reliable � getting the same measurement each time. � refers to how closely individual measurements agree with each other.

Accurate (accuracy) � capable of providing a correct reading or measurement. � correctly reflects the size of the thing being measured. � refers to how closely a measured value agrees with the correct value.

Accuracy � Accuracy is how close a measurement is to the correct data. � If an accepted value is 0. 9 and your measurements are 0. 87, 0. 92, 0. 91, and 0. 88 then those measurements are considered pretty accurate. Measurements of 0. 72 and 1. 14 are not as accurate.

Precision: “Significant Figures” Significant Figures are the number of reliably known digits in a number. It is the number of digits included in a number that are used to report the precision of a measurement. Significant figures are important because they tell us how precise the data we are using are. You will use what you learn about significant figures ALL year as you solve science problems involving mathematical calculations.

Examples � � � 13. 2 has 3 significant figures 13. 20 has 4 significant figures 45630 has 4 significant figures 708 has 3 significant figures 0. 453 has 3 significant figures 0. 091 has 2 significant figures 0. 620 has 3 significant figures 0. 00682 has 3 significant figures 1. 072 has 4 significant figures 300 has 1 significant figure 300. has 3 significant figures 300. 0 has 4 significant figures Using these examples, work in small groups to see if you can come up with a set of rules for determining how many significant figures are in any number….

What are the rules? Rules: � All non-zero digits are significant ◦ 1. 234 g has 4 significant figures ◦ 1. 2 g has 2 significant figures � Zeros between non-zero digits are significant ◦ 1002 kg has 4 significant figures ◦ 3. 07 m. L has 3 significant figures � Leading zeros to the left of the first nonzero digits are not significant; such zeroes merely indicate the position of the decimal point: ◦ 0. 001 o. C has only 1 significant figure ◦ 0. 012 g has 2 significant figures ◦ 0. 00530 has 3 significant figures � Zeros at the end of a decimal are significant ◦ 0. 0230 m. L has 3 significant figures ◦ 0. 20 g has 2 significant figures � All other zeros are not usually significant ◦ 2, 000 has 1 significant figure ◦ 2, 000. has 4 significant figures

Why does it work like this? The precision of the measurement is represented by the number of significant figures: � 0. 4 represents a measurement to the tenth’s place and has one significant figure � 0. 40 represents a measurement to the hundredth’s place and has two significant figures � 0. 400 represents a measurement to the thousandth’s place and has three significant figures � 200 represents a measure to the hundred’s place and is one significant figure � 200. represents a measure to the one’s place and has three significant figures.

Atlantic-Pacific Rule: The Atlantic-Pacific Rule is a mnemonic device used to help determine how many significant figures are in a number. Think of the number as being a map of the United States. To the left is the Atlantic Ocean, to the right is the Pacific Ocean. Rule: � If the decimal point is Present, start on the Pacific side and move east. Ignore all zeros on the Pacific side. Count significant digits starting with the first non-zero digit on the left: ◦ 0. 004703 has 4 significant figures ◦ 18. 00 also has 4 significant figures ◦ 400. has 3 significant figures � If the decimal point is Absent, start on the Atlantic side and move west. Start counting significant digits with the first nonzero digit on the right. ◦ 140, 000 has 2 significant figures ◦ 20060 has 4 significant figures ◦ 400 has 1 significant figure

Practice How many significant figures are there: � 3. 43 � 0. 005 � 240 � 6. 70 � 101. 0100 3 1 2 3 7

The Weakest Link In mathematical operations involving significant figures, the answer is reported in such a way that it reflects the reliability of the least precise operation. � Stated another way: a chain is no stronger than its weakest link. An answer can have no more significant digits than the least accurate measurement used. (The weakest link determines the answer). � Example 1: 2. 5 x 3. 42 - How many significant figures are in the answer and why? � Example 2: 2. 33 x 6. 085 x. 002 - How many significant figures in the answer and why? Example 1 - Two. The 2. 5 determines how many significant figures are in the answer because it is the least precise measurement - the “weakest link. ” Example 2 - One. The 0. 02 determines how many significant figures are in the answer because it is the least precise measurement - the “weakest link. ”

Problem Solving with Sig. Figs. � When adding or subtracting, your answer can only show as many decimal places as the measurement with the least number of places to the right of the decimal. ◦ 1. 2 + 12. 348 = 13. 5 (1 decimal place) � When multiplying or dividing, the answer should not have more significant figures than the number with the least amount of significant figures. ◦ 502 X 3. 6 = 1800 (2 significant figures)

Rounding Normal rounding rules apply EXCEPT: � If the digit used to determine rounding is a “ 5” then look at the place to be rounded. It must end up being an even number. ◦ If the digit to be rounded is even, round down. ◦ If the digit to be rounded is odd, round up. � Examples: ◦ ◦ Round 3. 78721 62. 5347 726. 835 24. 8514 to to 3 4 5 3 significant figures 3. 79 62. 53 726. 84 24. 8

Assignment � Complete the worksheet � All answers to all problems throughout the year will require you to understand apply rules for determining Significant Figures. Online Tutorial & Practice Problems available at: http: //www. fordhamprep. org/gcurran/sho/lessons/lesson 23. htm

It’s Friday! � 1. Initial roster � 2. Pick –up hand outs next to roster � 3. Take out lab and graph � 4. Warm-up: complete the ws with the snake