DETERMINING SIGNIFICANT
FIGURES
CRUNCHING NUMBERS WITH ACCURACY
AND PRECISION
BEFORE YOU CAN CRUNCH
2
 You must know which digits are significant
 Because they are going to control the number of
digits in a calculated figure
4/11/2020
WHAT IS A SIGNIFICANT FIGURE?
3
Significant figures are all the digits in a measurement
that are known with certainty plus a last digit that
must be estimated.
4/11/2020
WHICH NUMBERS ARE SIGNIFICANT?
4
For the purposes of significant figures there are two
major categories
 Nonzero digits:
1,2,3,4,5,6,7,8,9
 Zero digits:
0
4/11/2020
5
NONZERO
DIGITS
 All nonzero digits are significant
3269 cm – 4 significant figures
257 L – 3 significant figures
1.234567 mm – 7 significant figures
4/11/2020
6
ZEROES
Zeroes take three forms
Leading zeroes
Trapped zeroes
Trailing zeroes
4/11/2020
LEADING7 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
0.000012 m – 2 significant digits
0.003578 mL – 4 significant digits
4/11/2020
TRAPPED8 ZEROES
 Trapped zeroes are zeroes between two nonzero
digits. Trapped zeroes are always significant.
101 s – 3 significant figures
20013 m – 5 significant figures
0.3006 cm – 4 significant figures (the
leading zero is not significant)
4/11/2020
TRAILING9 ZEROES
 Trailing zeroes are zeroes that follow nonzero digits.
They are only significant if there is a decimal point in
the number.
0.1200 mm – 4 significant figures
3000 s – 1 significant figure
250. mL – 3 significant figures
50.000 g – 5 significant figures
4/11/2020
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.
4/11/2020
Examples of Exact Numbers
11
 2 in 2r
 3 and 4 in ¾ r3
 Avogadro’s number is exactly
6.02 x 1023
 One inch is exactly 2.54 cm
4/11/2020
Now you try
12
How many significant digits in each of the following:
1.034 s
0.0067 g
12 apples
3000 m
69 people
4/11/2020
Answers
13
 1.034 s




- 4 significant figures
0.0067 g - 2 significant figures
12 apples - exact number
3000 m - 1 significant figure
69 people - exact number
4/11/2020