1. Measurements Significant Figures Done By: Rania Moh’d-0115365 Renad Kharabsheh-0118448

2. Definition The term significant figures refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation. The number of significant figures in an expression indicates the confidence or precision of a quantity.

3. Where are they used? They are used both in calculations and measurements. Calculation: is the numerical values that ​​ are computed in various calculations. Such as addition, subtraction, multiplication, division and differential equations..... etc. Measurement: are the values ​​ resulting from the use of machines and devices: like the balance, the pH meter, thermal balance....... etc

4. Rules for Determining Significant Figures 1. Non-zero integers are considered significant. 2. All zeros located on the left of the number that is not zero are considered insignificant. These zeros serve only as space holders. They are there to put the decimal point in its correct location. They DO NOT involve measurement decisions. Upon writing the numbers in scientific notation (5.00 x 10¯ 3 and 3.040 x 10¯ 2 ), the non-significant zeros disappear. Example: number (0.00567) contains three significant figures (5,7,6).

5. Rules for Determining Significant Figures 3. All zeros between non-zero numbers are considered significant. Example: number (1.0075) Includes five significant figures (1,0,0,7,5) Another example: (0.0401) contains three significant figures (4,0,1).

6. Rules for Determining Significant Figures 4. All zeros located to the right of the figure, which includes a decimal point are considered significant. Example: (0.00590) contains three significant figures (5,9,0) 5. All zeros, located to the right of the correct number, which does not contain a decimal point may be considered significant and may be considered all or some insignificant. This depends on the used units of measurement and the measurement accuracy. Example: the number (300) cm

7. More Examples The table shows several examples of numbers written in standard decimal notation (first column) and in scientific notation (second column). The third column shows the number of significant figures in the corresponding expression in the second column. Decimal ExpressionScientific NotationSignificant Figures 1,222,000.001.222 x 10 6 4949 1.22200000 x 10 6 -0.0000000100 -1 x 10 -8 1313 -1.00 x 10 -8

8. Calculations and Significant Figures In mathematical operations involving significant figures, the answer is reported in such a way that it reflects the reliability of the least precise operation. Let's state that another way: a chain is no stronger than its weakest link. An answer is no more precise that the least precise number used to get the answer. Let's do it one more time: imagine a team race where you and your team must finish together. Who dictates the speed of the team? Of course, the slowest member of the team. Your answer cannot be MORE precise than the least precise measurement.

9. Calculations and Significant Figures Addition and Subtraction: For addition and subtraction, look at the decimal portion(i.e., to the right of the decimal point) of the numbers ONLY. Here is what to do: 1) Count the number of significant figures in the decimal portion of each number in the problem. (The digits to the left of the decimal place are not used to determine the number of decimal places in the final answer.) 2) Add or subtract in the normal fashion. 3) Round the answer to the LEAST number of places in the decimal portion of any number in the problem.

10. Example 13.214 + 234.6 + 7.0350 + 6.38 Looking at the numbers, I see that the second number, 234.6, is only accurate to the tenths place; all the other numbers are accurate to a greater number of decimal places. So my answer will have to be rounded to the tenths place: 13.214 + 234.6 + 7.0350 + 6.38 = 261.2290 Rounding to the tenths place, I get: 13.214 + 234.6 + 7.0350 + 6.38 = 261.2

11. Calculations and Significant Figures Multiplication and Division: The following rule applies for multiplication and division: The LEAST number of significant figures in any number of the problem determines the number of significant figures in the answer. This means you MUST know how to recognize significant figures in order to use this rule.

12. Examples Example #1: 2.5 x 3.42. The answer to this problem would be 8.6 (which was rounded from the calculator reading of 8.55). Why? 2.5 has two significant figures while 3.42 has three. Two significant figures is less precise than three, so the answer has two significant figures.