Significant Digits Significant digits in measurements and calculations

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Significant Digits Significant digits in measurements and calculations

Significant Digits Significant digits in measurements and calculations

Accuracy & Precision Accuracy- describes how well the results of a measurement agree with

Accuracy & Precision Accuracy- describes how well the results of a measurement agree with an accepted value Precision- the degree of exactness of a measurement, depends on the instrument used for measurement

Significant Digits in Measurements n There are five rules or guidelines that should be

Significant Digits in Measurements n There are five rules or guidelines that should be applied in determining whether a digit in a measurement is significant.

Rule #1 n Every nonzero digit in a measurement is always significant. n Example:

Rule #1 n Every nonzero digit in a measurement is always significant. n Example: 24. 7 m 3 significant digits 715. 55 g 5 significant digits

Rule #2 n Zeros appearing between nonzero digits are significant. n Example: 7003 m

Rule #2 n Zeros appearing between nonzero digits are significant. n Example: 7003 m 4 significant digits 1. 503 g 4 significant digits 40. 079 g 5 significant digits

Rule #3 n Leading zeros are never significant. They serve as placeholders only. n

Rule #3 n Leading zeros are never significant. They serve as placeholders only. n Example: 0. 0071 m 2 significant digits 0. 421 m 3 significant digits 0. 000 099 m 2 significant digits

Rule #4 n Trailing zeros are only significant if the decimal point is written.

Rule #4 n Trailing zeros are only significant if the decimal point is written. n Example: 70 m 1 significant digit 70. 0 m 3 significant digits 27, 000 cm 2 significant digits

Rule #5 n Counting numbers and exactly defined quantities have an unlimited number of

Rule #5 n Counting numbers and exactly defined quantities have an unlimited number of significant digits. n Example: 20 books ∞ number 1 hour = 60 minutes ∞ number

Review How many significant digits are in each of the following measurements? a. 123

Review How many significant digits are in each of the following measurements? a. 123 m b. 0. 123 m c. 40. 506 m d. 98 00. 0 m e. 22 metersticks f. 30 m g. 0. 07080 m h. 98 000 m n

Significant Figures in Calculations n Calculated values must be rounded so that they are

Significant Figures in Calculations n Calculated values must be rounded so that they are consistent with the measurements from which they were calculated.

Multiplication and Division In calculations involving multiplication and division, answers should be rounded so

Multiplication and Division In calculations involving multiplication and division, answers should be rounded so that they contain the same number of significant digits as the measurement with the least number of significant digits. n Example: 7. 55 m x 0. 34 m = 2. 4526 m / 8. 4 m = n

Addition and Subtraction The answer to an addition or subtraction calculation should be rounded

Addition and Subtraction The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places. n Example: 12. 52 m + 349. 0 m + 8. 24 m = 74. 626 m – 28. 34 m = n

Review n n n Measure and calculate the length of the perimeter of your

Review n n n Measure and calculate the length of the perimeter of your note card. Round your answer to the correct number of significant digits. Measure and calculate the area of your note card (length x width). Round your answer to the correct number of significant digits. Calculate the number of minutes spent in school in a 5 day week.

Quiz: Significant Digits

Quiz: Significant Digits

How many significant digits are in each of the measurements below: 1) 100 m

How many significant digits are in each of the measurements below: 1) 100 m 2) 0. 0230 m/s 3) 100. 1 m 4) 2. 0 x 1011 m/s 5) 50 metersticks 6) 10. 380 s Solve the following problems and round to the correct number of significant digits. 7) 3. 42 cm + 8. 13 cm 8) 0. 00457 cm x 0. 18 cm 9) 85. 0869 m 2 ÷ 9. 0049 m 10) 13. 80 cm – 6. 0741 cm Write the following number in correct scientific notation. 11) 0. 00010500 µm