Significant Figures Counting is not the same as

Significant Figures • Counting is not the same as measuring. If you want to know the number of beans in a jar you can count them and know exactly. If you want to measure the length of a pencil however, you can use a ruler or some other finer instrument, but the length can never be determined exactly.

What is the length of the pencil?

What is the length of the pencil? • The length of the pencil is between 15 cm and 16 cm. If we looked very closely we might be able to use the ruler to determine the length is closer to 15. 7 cm than it is to either 15. 8 cm or 15. 6 cm.

What is the length of the pencil? • In this case we think the length is 15. 7 ±. 1 cm. • We can claim that all three digits are significant, the 1, the 5 and even the 7. • We could not measure any significant figures beyond the 7.

What is the length of the pencil? • If we had a ruler with more markings on it, for example millimeters, we could report more significant figures.

What is the length of the pencil? • The length 15. 7 cm can alternately be written as or. 157 m or 157 mm or 157, 000µm or 157, 000 nm, but recording a measurement this way could be misleading.

What is the length of the pencil? • • • 15. 7 cm. 157 mm 157, 000 µm 157, 000 nm • The first numbers on the left indicate 3 significant figures. They indicate that we know the length to a certain level of accuracy. The micrometer and nanometer numbers could have up to 6 and 9 significant figures respectively.

What is the length of the pencil? • • • 15. 7 cm. 157 mm 157, 000 µm 157, 000 nm • When we cannot determine the exact number of significant figures, we presume that fewest number of significant figures possible.

What is the length of the pencil? • • 15. 7 cm. 157 mm 157, 000 µm 157, 000 nm. 000157 km. 0001570 km • The second to last number recorded on the bottom in kilometers may at first seems to be indicating a large number of significant figures, but it is in fact only indicating 3 significant figures. • The leading zeros are not significant. • The final number is reported to 4 significant figures because trailing zeros are significant.

Scientific Notation and Significant Figures How many significant figures do each of these numbers have below? • • 486, 000 200 3, 000. 0015 207. 15. 000 035. 0010

Scientific Notation and Significant Figures Write these in scientific notation. • • 486, 000 200 3, 000. 0015 207. 15. 000 035. 0010

Scientific Notation and Significant Figures • Additional Examples

Processing Significant Figures • When you are adding, subtracting, multiplying or dividing you must first make sure you are using units consistently.

Processing Significant Figures • When you are adding, subtracting, multiplying or dividing you must first make sure you are using units consistently.

Processing Significant Figures • When you are adding, subtracting, multiplying or dividing you must first make sure you are using units consistently. • If you are adding meters to kilometers make sure you are converting one of them so that you are only using one set of units. The conversion will not change the number of significant figures.

Processing Significant Figures • 10. 3 km • 801 m • How many significant figures before and after conversion?

Processing Significant Figures • 10. 3 km • 1. 03 X 10^4 m • 801 m • 0. 801 km • How many significant figures before and after conversion?

Processing Significant Figures • Example: 3, 150 + 259. 1 • Adding and subtracting using significant figures.

Processing Significant Figures • Example: 3, 150 + 259. 1 • Adding and subtracting using significant figures. • 1. ) Make sure the units are correct. Convert them if necessary.

Processing Significant Figures • Example: 3, 150 + 259. 1 • Done • Adding and subtracting using significant figures. • 1. ) Make sure the units are correct. Convert them if necessary.

Processing Significant Figures • Example: 3, 150 + 259. 1 • Done • Adding and subtracting using significant figures. • 1. ) Make sure the units are correct. Convert them if necessary. • 2. ) Create a place value scaffold for the problem.

Processing Significant Figures • Example: 3, 150 + 259. 1 • Done . + . • Adding and subtracting using significant figures. • 1. ) Make sure the units are correct. Convert them if necessary. • 2. ) Create a place value scaffold for the problem.

Processing Significant Figures • Example: 3, 150 + 259. 1 • Done + 3 1 5 2 5 9 . . 1 . • Adding and subtracting using significant figures. • 1. ) Make sure the units are correct. Convert them if necessary. • 2. ) Create a place value scaffold for the problem. • 3. ) Put only the significant figures in the place value scaffold.

Processing Significant Figures • 4. ) Add the numbers without regards to significant figures + 3 1 5 2 5 9 . . 1 .

Processing Significant Figures • 4. ) Add the numbers without regards to significant figures + 3 1 5 2 5 3 3 0 9 9 . . 1

Processing Significant Figures + 3 1 5 2 5 3 3 0 9 9 . . 1 • 4. ) Add the numbers without regards to significant figures • 5. )Determine which of the decimal places are significant figures.

Processing Significant Figures Starting from the left, the first figure will always be significant. After that the first figure that cant be determined is the last significant figure. + 3 1 5 2 5 3 3 0 9 9 . . 1 • 4. ) Add the numbers without regards to significant figures • 5. )Determine which of the decimal places are significant figures.

Processing Significant Figures Starting from the left, the first figure will always be significant. After that the first figure that cant be determined is the last significant figure. + 3 1 5 2 5 3 3 0 9 9 . . 1 • 4. ) Add the numbers without regards to significant figures • 5. )Determine which of the decimal places are significant figures.

Processing Significant Figures Starting from the left, the first figure will always be significant. After that the first figure that cant be determined is the last significant figure. + 3 1 5 2 5 3 3 0 9 9 . . 1 • 4. ) Add the numbers without regards to significant figures • 5. )Determine which of the decimal places are significant figures.

Processing Significant Figures Starting from the left, the first figure will always be significant. After that the first figure that cant be determined is the last significant figure. + 3 1 5 2 5 3 3 0 9 9 . . 1 • 4. ) Add the numbers without regards to significant figures • 5. )Determine which of the decimal places are significant figures.

Processing Significant Figures Starting from the left, the first figure will always be significant. After that the first figure that cant be determined is the last significant figure. + 3 1 5 2 5 3 3 0 9 9 . . 1 • 4. ) Add the numbers without regards to significant figures • 5. )Determine which of the decimal places are significant figures.

Processing Significant Figures Starting from the left, the first figure will always be significant. After that the first figure that cant be determined is the last significant figure. + 3 1 5 2 5 3 3 0 9 9 . . 1 • 4. ) Add the numbers without regards to significant figures • 5. )Determine which of the decimal places are significant figures.

Processing Significant Figures Starting from the left, the first figure will always be significant. After that the first figure that cant be determined is the last significant figure. + 3 1 5 2 5 3 3 0 9 9 . . 1 • 4. ) Add the numbers without regards to significant figures • 5. )Determine which of the decimal places are significant figures. • 6. ) You can only report the significant figures, so, round.

Processing Significant Figures Starting from the left, the first figure will always be significant. After that the first figure that cant be determined is the last significant figure. + 3 1 5 2 5 3 3 0 9 9 . . 1 3 1 • 4. ) Add the numbers without regards to significant figures • 5. )Determine which of the decimal places are significant figures. • 6. ) You can only report the significant figures, so, round.

Blank Place Value Scaffold +

Processing Significant Figures • Adding and subtracting

Processing Significant Figures 3. 0 x 10^3 m + 2. 5 x 10^1 m If we weren’t concerned with significant figures we would rewrite this as 3000 m + 25 m = 3025 m This result however would have 4 significant figures. We cant report the sum this way because we only ever measured anything to 2 significant figures. The figure that we showed as 3000 m might actually be 3040 m or 2950 m and because of this we cant claim the sum is known to be 3025 m

Processing significant figures • Addition examples • 9. 0210 x 10^4 m + 8. 3357 x 10^3 m

Processing significant figures • Addition examples • 8. 543 x 10^4 m + 4. 123 x 10^2 m + 3. 15 x 10^1 m

Processing significant figures • Addition examples • 103. 21 m +. 0003 m + 1. 204 x 10^3 m

Processing Significant Figures • Multiplication and Division

Processing Significant Figures • Multiplication and Division • For our purposes, we will use this process: 1. ) Find the number of significant figures of each factor. 2. ) Multiply the factors without regard to significant figures. 3. ) Round the product. Only use as many significant figures as are had by the factor with the fewest significant figures.

Processing Significant Figures • Example: What is the area of a rectangular field with the following measurements? 552 m x 3100 m

Processing Significant Figures • Example: What is the area of a rectangular field with the following measurements? 552 m x 3100 m 552 m how many sig figs? X 3100 m how many sig figs?

Processing Significant Figures • Example: What is the area of a rectangular field with the following measurements? 552 m x 3100 m 552 m how many sig figs? 3 X 3100 m how many sig figs? 2

Processing Significant Figures •

Processing Significant Figures •

Processing Significant Figures • Example: What is the volume of rectangular prism with a height of 101 cm, a length of 8 cm and a width of 27 cm?

Processing Significant Figures • Example: What is the volume of a cylinder with a height of 12. 0 cm and a radius of 6. 2 cm?