1. DETERMINING SIGNIFICANT FIGURES
Crunching numbers with accuracy and precision

2. BEFORE YOU CAN CRUNCH You must know which digits are significant
Because they are going to control the number of digits in a calculated figure
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3. WHAT IS A SIGNIFICANT FIGURE?
Significant figures are all the digits in a measurement that are known with certainty plus a last digit that must be estimated.
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4. WHICH NUMBERS ARE SIGNIFICANT?
For the purposes of significant figures there are two major categories
Nonzero digits:
1,2,3,4,5,6,7,8,9
Zero digits:
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5. NONZERO DIGITS All nonzero digits are significant
3269 cm – 4 significant figures
257 L – 3 significant figures
mm – 7 significant figures
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6. ZEROES Zeroes take three forms Leading zeroes Trapped zeroes
Trailing zeroes
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7. LEADING ZEROES
Leading zeroes are zeroes that come before the nonzero digits in a number. They are place holders only and are never considered significant.
0.123 L – 3 significant digits
m – 2 significant digits
mL – 4 significant digits
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8. TRAPPED ZEROES
Trapped zeroes are zeroes between two nonzero digits. Trapped zeroes are always significant.
101 s – 3 significant figures
20013 m – 5 significant figures
cm – 4 significant figures (the leading zero is not significant)
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9. TRAILING ZEROES
Trailing zeroes are zeroes that follow nonzero digits. They are only significant if there is a decimal point in the number.
mm – 4 significant figures
3000 s – 1 significant figure
250. mL – 3 significant figures
g – 5 significant figures
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10. Exact Numbers
Numbers that were not obtained using measuring devices but by counting.
They can also arise from definitions.
They can be assumed to have an infinite number of significant figures.
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11. Examples of Exact Numbers
2 in 2r
3 and 4 in ¾ r3
Avogadro’s number is exactly x 1023
One inch is exactly 2.54 cm
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12. Now you try How many significant digits in each of the following:
12 apples
3000 m
69 people
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13. Answers 1.034 s - 4 significant figures
g significant figures
12 apples exact number
3000 m significant figure
69 people exact number
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14. Process for Addition/Subtraction
Step #1: Determine the number of decimal places in each number to be added/subtracted.
Step #2: Calculate the answer, and then round the final number to the least number of decimal places from Step #1.

15. Addition/Subtraction Examples
Round to tenths place.
Example #2:
Round to hundredths place.
Example #3:
Round to ones place.
23.456
24.706
Rounds to:
24.7
3.56
2.0699
2.07 14
26.735 27

16. Process for Multiplication/Division
Step #1: Determine the number of sig figs in each number to be multiplied/divided.
Step #2: Calculate the answer, and then round the final number to the least number of sig figs from Step #1.

17. Multiplication/Division Examples
Round to
1 sig fig.
Example #2:
2 sig figs.
Example #3:
3 sig figs.
23.456 x x
Rounds to: 1
3.56 x x
0.67
14.0/
11.73
1.19

18. Practice Example #1: Example #2: Example #3: . 23.456 x 4.20 x 0.010
Rounds to: ?
0.001
17/
22.73