Transcript Adding and Subtracting Using Significant Figures

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:
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 .7287
11.73 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 10-5g + 8.269 X 10-6g =
• 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
Rule: addition using a calculator
3.76 X 10-5g + 8.269 X 10-6g =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 X10-5g
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
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 10-4g – 1.457 X 10-6g =
• Enter the into the calculator
2.5 X (exp) -4 – 1.457 X (exp) -6
Enter
You get 2.48543 X 10-4
Rounding using a calculator
2.5 X 10-4g – 1.457 X 10-6g =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 X10-5g
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
1.
2.
3.
4.
5.
6.
2.57 mL + 45.3 mL =
0.034 g + 1.3 g =
9.9 X 10-3cm + 1.01 X 10-2cm =
7.03427 X 101 m – 3.4 X 10-3 m =
3.657 kg – 2.99 kg =
7.54 X 10-9 L – 5.43 X 10-12 L =
Answers Practice problems
1.
2.
3.
4.
5.
6.
47.8 mL
1.3 g
2.00 X 10-2 cm
70.3393 m
0.67 kg
7.53 X 10-9 L