The Science of Physics Chapter #1 Ms. Hanan Anabusi

1-2 Measurements in Experiments Objectives List basic SI units and the quantities they describe. Convert measurements into scientific notation. Distinguish between accuracy and precision. Use significant figures in measurements and calculations.

Accuracy: This is the concept which deals with whether a measurement is correct when compared to the known value or standard for that particular measurement. When a statement about accuracy is made, it often involves a statement about percent error. Percent error is often expressed by the following equation: % error = (|experiment value - accepted value| / accepted value) x 100%

Precision: This is the concept which addresses the degree of exactness when expressing a particular measurement. The precision of any single measurement that is made by an observer is limited by how precise the tool (measuring instrument) is in terms of its smallest unit. How would you divide the following 1 meter long bar up into smaller divisions? Why? What would your choice have to do with precision? 1 METER BAR

Precision and Measuring:

Significant Digits What are they? And How do you use them?

Significant Digits: When someone else has made a measurement, you have no control over the choice of the measuring tool or the degree of precision associated with the device used. You must rely on a set of rules to tell you the degree of precision.

8 Significant Digits The number of digits reported in a measurement reflect the accuracy of the measurement and the precision of the measuring device. All the figures known with certainty plus one extra digit are called significant digits or figures. In any calculation, the results are reported to the fewest significant figures (for multiplication and division) or fewest decimal places (addition and subtraction).

9 Significant Digits Rules for Identifying the Number of Significant Digits. Non-zero numbers are always significant (1 to 9). Zeros found between non-zero numbers are always significant. Zeros to the right of both a decimal place and a significant digit are significant. Zeros that are used solely as placeholders are not considered significant.

10 Significant Digits Examples for Determining the Number of Significant Digits 453 has three significant digits, because of rule one. Each digit is a “non-zero” digit has four significant digits, because of rules one and two. The “3” and the “7” are non-zero digits, and both zeros are found in-between two other significant digits has four significant digits, because of rules one and three. The “3” and the “5” are non-zero digits, and both zeros are found to the right of both a decimal and a significant digit.

11 Significant Digits Examples for Determining the Number of Significant Digits has one significant digit, because of rules one and four. The “8” is a nonzero digit and is significant. The four zeros shown in the number are just placeholders. Remember, rule three says that the zeros must be to the right of both a decimal place and a significant digit to be considered significant.

12 Significant Digits Examples for Determining the Number of Significant Digits 400 has only one significant digit because of rules one and four. The “4” is a non-zero digit, making it significant. The two zeros are not covered by rules two or three, so they are merely placeholders x 10 3 has three significant digits, because of rules one and three. The “4” is a non-zero digit and the two zeros are shown to the right of both a decimal place and a significant digit.

13 Significant Digits Student Challenge. Identify the number of significant digits shown in each of the following examples. A) 2593 significant digits. B) significant digits C) significant digits D) 4.50 x significant digits E) significant digit

14 Significant Digits Rule for Multiplication and Division For multiplication and division, your answer must show the same number of significant digits as the measurement in the calculation with the least number of significant digits.

15 Significant Digits Rule for Multiplication and Division For example, 3.40 cm x cm x cm = cm 3 before rounding We, can’t report an answer with seven significant digits if the measurement with the least number of significant digits in our calculation, 3.40 cm, shows only three significant digits. We must round our answer to three significant digits, giving us a rounded answer of 782 cm 3.

16 Significant Digits Rule for Addition and Subtraction For addition and subtraction, your answer must show the same number of decimal places as the number in the calculation with the least number of decimal places.

17 Significant Digits Rule for Addition and Subtraction For example, m/s – 8.07 m/s = m/s In this example, our answer would be correct as shown. The measurement with the least number of decimal places, 8.07 m/s, is reported to the hundredths place. Our answer must also be reported to the hundredth place as m/s.

18 Significant Digits Rule for Addition and Subtraction For example, m/s – 8.07 m/s = m/s In this example, our answer would be correct as shown. The measurement with the least number of decimal places, 8.07 m/s, is reported to the hundredths place. Our answer must also be reported to the hundredth place as m/s.

19 Significant Digits Use of Scientific Notation to Show the Proper Number of Significant Digits There will be times when you see answers that are written in scientific notation, and you might not be sure why. Often, answers are written in scientific notation just to express the answer in the correct number of significant digits.

20 Significant Digits Use of Scientific Notation to Show the Proper Number of Significant Digits Look at the following example. 8.0 m x 50.0 m = 400 m 2 The measurement in this calculation with the least number of significant digits, 8.0 m, shows two significant digits. Our answer only shows one significant digit. We can write this answer in scientific notation just for the purpose of showing the same value with two significant digits. Our answer would be expressed as 4.0 x 10 2 m 2.

21 Significant Digits Use of Scientific Notation to Show the Proper Number of Significant Digits A second method for showing additional significant digits involves using a decimal at the right of a significant digit of zero. For example, if you wanted to show the number 700 with three significant digits, you could put a decimal point to the right of the second zero, as in “700.” or you could use either of the other two methods described here. For this book, we will be using decimals and/or the scientific notation method.

22 Significant Digits Summary Rules for Identifying the Number of Significant Digits. Non-zero numbers are always significant. Zeros found between non-zero numbers are always significant. Zeros to the right of both a decimal place and a significant digit are significant. Zeros that are used solely as placeholders are not considered significant. Rule for Addition and Subtraction For addition and subtraction, your answer must show the same number of decimal places as the number in the calculation with the least number of decimal places. Rule for Addition and Subtraction For addition and subtraction, your answer must show the same number of decimal places as the number in the calculation with the least number of decimal places.

Section Review Page 20 Questions 1, 2, 3, and 4 Odd questions (1 and 3) as class-work, and Even questions (2, and 4) as homework