1. Adding and Subtracting Using Significant Figures How many digits are significant and how do you know?

2. Covered in this Lesson This lesson will demonstrate how to add/subtract measurements and report the result to the correct number of significant figures (sig figs). – When adding or subtracting the place value of the least accurate number determines the number of sig figs.

3. Rule: addition Your answer is expressed to the place value the same as the least accurate number in the problem. Example: 8.2087 mL + 2.430 mL + 0.09 mL = Notice the 0.09 is only to the hundredths and the least accurate so our answer is expressed to the hundredths. 8.2087 mL 2.430 mL 0.09 mL 11.728711.73 mL

4. Rule: addition using a calculator Do the calculation as normal, then round to the least accurate number. (exp = power of 10) Try this: 3.76 X 10 -5 g + 8.269 X 10 -6 g = Enter the into the calculator 3.76 X (exp key) -5 + 8.269 X (exp key) -6 Press Enter You get 4.5869 X10 -5

5. Rule: addition using a calculator 3.76 X 10 -5 g + 8.269 X 10 -6 g =4.5869 X10 -5  Determine the least accurate from the given numbers and round to the same place.  3.76 X 10 -5 is the least accurate you round to the same accuracy.  Answer: 4.59 X10 -5 g

6. Rule: subtraction This is the same as for addition, your answer is expressed to the place value the same as the least accurate number in the problem Example: 5.157 m – 3 m = Notice the 3 is to the ones and the least accurate so our answer is expressed to the ones. 5.157 m –3. m 2.157 m 2m

7. Rule: subtracting using a calculator Do the calculation as normal, then round to the least accurate number. (exp = power of 10) Try this: 2.5 X 10 -4 g – 1.457 X 10 -6 g = Enter the into the calculator 2.5 X (exp) -4 – 1.457 X (exp) -6 Enter You get 2.48543 X 10 -4

8. Rounding using a calculator 2.5 X 10 -4 g – 1.457 X 10 -6 g =2.48543 X 10 -4  Determine the least accurate from the given numbers and round to the same place.  2.4 X 10 -4 this is the lease accurate, round to the same accuracy.  Answer: 2.5 X10 -5 g

9. Rule: addition or subtracting with an exact number Do the calculation as normal, the exact number does not affect the number of significant figures. Examples: 3 pies + 7 pies + 4 pies = 14 pies 4 cookies – 2 cookies = 2 cookies

10. Practice problems 1.2.57 mL + 45.3 mL = 2.0.034 g + 1.3 g = 3.9.9 X 10 -3 cm + 1.01 X 10 -2 cm = 4.7.03427 X 10 1 m – 3.4 X 10 -3 m = 5.3.657 kg – 2.99 kg = 6.7.54 X 10 -9 L – 5.43 X 10 -12 L =

11. Answers Practice problems 1.47.8 mL 2.1.3 g 3. 2.00 X 10 -2 cm 4.70.3393 m 5.0.67 kg 6.7.53 X 10 -9 L