1 / 11

Significant Figures

Significant Figures. Significant figures – Not a mathematical concept A concept of measurement and precision. Significant figures indicate the maximum precision available for a measurement or calculation. .

junior
Download Presentation

Significant Figures

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Significant Figures Significant figures – Not a mathematical concept A concept of measurement and precision Significant figures indicate the maximum precision available for a measurement or calculation. A measurement cannot be more precise than the available measurement tool. A calculated value cannot be more precise than the least precise numerical values used in the calculation.

  2. Significant Figures Assume you have two digital scales of different quality, and you measure the same quartz crystal on each scale 1. The cheapest scale reads in grams to 2 decimal places The mass for the crystal reads 02.04 g 2. A more expensive scale reads to 3 decimal places The mass for the crystal reads 02.040 g

  3. Significant Figures The two values obtained for the quartz crystal are: 02.04 g and 02.040 g The two values are equal mathematically, but they are not equal in precision the 02.040 value is more precise The presence of the trailing zero is important or significant in communicating this increased precision, even though it is not important mathematically

  4. Significant Figures The concept of significant figures is used to evaluate the precision of a measurement. For the two values obtained for the quartz crystal: 02.04 g has 3 significant figures The leading zero is not significant since it provides no additional precision in the measurement 02.040 g has 4 significant figures The trailing zero is significant since it indicates an increase in the precision of the measurement

  5. A measurement cannot be more precise than the available measurement tool. If the measurement tool has an analog scale, the measurement value is estimated to one additional digit beyond the designated scale. If the measurement tool has a digital scale, the measurement value has the same number of significant figures as the digital readout.

  6. A calculated value cannot be more precise than the least precise numerical values used in the calculation. In adding and subtracting, the calculated value will have no more decimal places than the data point with the fewest decimal places Example: The sum of the following measurements: 235.05 cm + 19.68 cm + 2.1 cm = 256.8 cm 2.1 has only one decimal place so the sum can only be accurate to one decimal place.

  7. A calculated value cannot be more precise than the least precise numerical values used in the calculation. In multiplying and dividing, the calculated value will have no more total significant figures than the than the data point with the fewest significant figures. Example: The volume of a box measuring: 35.5 cm x 1.976 cm x .25 cm = 17 cm 3 .25 has only two significant figures so the answer can only have two significant figures. Recognize the difference between counting decimal places for addition/subtraction and counting significant figures for multiplication/division.

  8. Counting Significant Figures 1. Non-zero numbers are always significant 2. Preceding zeros are never significant. Preceding zeros are those that precede all of the non-zero numbers in a value. The can lie before or after a decimal point. 3. Embedded zeros are always significant. Embedded zeros are those in between two non-zero numbers in a value. 4. Trailing zeros are not significant unless there is an explicit decimal point in the value. Trailing zeros are those that follow all of the non-zero numbers.

  9. Examples: 0.002050 has 4 significant figures. a) There are 2 non-zero numbers which are significant. b) There is 1 embedded zero which is significant. c) There is 1 trailing zero which is significant since there is a decimal point in the value. d) There are 3 preceding zeros which are not significant. 1067800 has 5 significant figures. a) There are 4 non-zero numbers which are significant. b) There is 1 embedded zero which is significant. c) There are 2 trailing zero which are not significant since there is no decimal point in the value. d) There are no preceding zeros.

  10. Examples: Your calculator produces a value of 0.00574456 for a calculation. Convert the value to two significant figures. a) Only consider one more figure than is required, and ignore any remaining figures – they can be dropped or if necessary changed to non-significant zeros as placeholders. 0.005744 b) The fourth number is a 4, so in converting to two significant figures, the fourth number can be dropped. Final answer is 0.00574

  11. Examples: Your calculator produces a value of 256,841 for a calculation. Convert the value to three significant figures. a) Only consider one more figure than is required, and ignore any remaining figures – they can be dropped or if necessary changed to non-significant zeros as placeholders. 256,800 b) The fourth number is an 8, so in converting to three significant figures, the third number must be rounded up and the fourth number is converted to non- significant zero as a place holder. Final answer is 257,000

More Related