SIGNIFICANT
FIGURES
Significant Figures
• These are the number of digits in a value that represents the degree of
accuracy of the value.
• The length of the pencil shown below is between 18.7 and 18.8 cm. We know
it hasn’t reached 18.8 so we can accurately record its length as 18.7 cm. Any
value in between is just an estimate. Therefore the degree of accuracy of this
ruler is 3 significant figures.
Rules for Significant Figures
1. ALL non-zero digits are significant. (2557 has 4 sig. fig)
2. ALL zeroes between non-zero digits are significant. (30008 has 5 sig. fig.)
3. ALL zeroes that are SIMULTANEOUSLY to the right of a decimal point and at
the end of a number are always significant. (98.0 has 3 sig. fig)
4. Leading zeroes that are to the left of the first non-zero digits are NOT
significant. (0.057 has 2sig. fig)
5. When a number ends in zeroes, i.e. there are no decimal points, the zeroes
are not necessarily significant. (5600 has 2,3 or 4 sig fig)
“When a number ends in zeroes, i.e. there are no decimal points, the
zeroes are not necessarily significant”.
• We must not change the place value of the number when expressing in
significant figures.
• Example: express $56 782 to two (2) significant figures
Questions:
1. How many significant figures do the following numbers have?
a) 30.9
b) 5588
c) 276.00
d) 8 000 000
e) 0.0044
f) 0.05002
Expressing Significant Figures to
Desired Accuracy
• Example 1 : Express 87 643 to two (2) significant figures.
Answer:
88 000
• Example 2: Express 0.006639 to one (1) significant figure.
Answer:
0.007
Questions:
1. Express the following digits to the number of significant figures indicated
in bracket.
a) 4569 [1 sig fig] =
b) 0.00846 [2 sig fig] =
c) 0.9649 [1 sig fig] =
d) 99.57 [1 sig fig] =
e) 76.03 [ 3 sig fig] =
f) 0.90085 [ 3 sig fig] =
Correct Way for Expressing Answers
• When values or multiplied or divided the answer is expressed as the least
number of significant figures given.
Example: 25.28 𝑚 × 17.0 𝑚 = 429.76 𝑚2 [3 sig fig]
= 𝟒𝟑𝟎 𝒎𝟐
• When values are added or subtracted, the answer is expressed as the least
number of decimal places given.
Example: 98.5 𝑔 + 12.276 𝑔 − 20.18 𝑔 = 90.596 [1 d.p.]
= 90.6 g