Significant digits in measurements and calculations

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

Rule #1 Every nonzero digit in a measurement is always significant. Example: 24.7 m 3 significant digits 715.55 g 5 significant digits

Rule #2 Zeros appearing between nonzero digits are significant. Example: 7003 m 4 significant digits 1.503 g 40.079 g 5 significant digits

Rule #3 Leading zeros are never significant. They serve as placeholders only. Example: 0.0071 m 2 significant digits 0.421 m 3 significant digits 0.000 099 m

Rule #4 Trailing zeros are only significant if the decimal point is written. Example: 70 m 1 significant digit 70.0 m 3 significant digits 27, 000 cm 2 significant digits

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

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

Significant Figures in Calculations 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 that they contain the same number of significant digits as the measurement with the least number of significant digits. Example: 7.55 m x 0.34 m = 2.4526 m / 8.4 m =

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. Example: 12.52 m + 349.0 m + 8.24 m = 74.626 m – 28.34 m =

Putting it All Together 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.

Question #1 Form a number that is between 400 and 500 containing 2 significant digits.

Question #2 Form a number that is less than 1, has 4 digits, and has only 3 significant figures.

Question #3 What is the answer to the problem 63.4 x 14 rounded to the correct number of significant digits?

Question #4 What is the answer to the problem 61.0 ÷ 9.1 rounded to the correct number of significant digits?

Question #5 What is the answer to the problem 60 + 83.2 rounded to the correct number of significant digits?

Question #6 Form a number that is greater than 1000 having 6 significant digits.

Question #7 What is the answer to the problem 0.158 + 0.4 rounded to the correct number of significant digits?

Question #8 Form a number containing 3 zeros that has 4 significant digits.

While waiting for the bell to ring, Pick up handouts. Get out note taking guide from yesterday and complete the remaining problems as review. After completing the review problems, get out the homework assigned yesterday and identify any problems about which you have questions.

Write the following number in correct scientific notation. 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 m2 ÷ 9.0049 m 10) 13.80 cm – 6.0741 cm Write the following number in correct scientific notation. 11) 0.00010500 µm