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

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.

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

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 g X g = Enter the into the calculator 3.76 X (exp key) X (exp key) -6 Press Enter You get X10 -5

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

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: m – 3 m = Notice the 3 is to the ones and the least accurate so our answer is expressed to the ones m –3. m m 2m

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 g – X g = Enter the into the calculator 2.5 X (exp) -4 – X (exp) -6 Enter You get X 10 -4

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

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

Practice problems mL mL = g g = X cm X cm = X 10 1 m – 3.4 X m = kg – 2.99 kg = X L – 5.43 X L =

Answers Practice problems mL g X cm m kg X L