Significant Digits
Significant digits are widely used in science to communicate the preciseness of a
measurement. The more significant digits a stated measurement has, the more precise
it is.
1. Which digit(s) in a number are significant?
Rule
All non-zero digits (i.e. digits
from 1 to 9) are significant.
Zero digit(s) located between
two non-zero digits are
significant.
Zero digit(s) located to the right
of a decimal point is/are
significant.
Zero digit(s) located to the left
of significant digits is/are NOT
significant.
Zero digit(s) located to the right
of other significant digits in the
whole number part is/are NOT
significant.
Example
14.5 has three significant digits. All the digits in this
number are significant.
10.05 has four significant digits. The digits 1 and 5
are significant because they are non-zero digits. The
two 0s are significant because they are located
between two non-zero digits.
98.0 has three significant digits. The digits 9 and 8
are significant because they are non-zero digits. The
0 is significant because it’s located to the right of the
decimal point.
TIP: A good way to remember this rule is that without
the 0, the value of the number would remain the
same (i.e. 98 is the same value as 98.0). The reason
for including the trailing 0 is to show that it’s
significant.
0.0067 has two significant digits. The digits 6 and 7
are significant because they are non-zero digits. The
0s are NOT significant because they are located to
the left of the significant digits 6 and 7.
TIP: In this case the 0s are included to show the
value (i.e. how small) the number (measurement) is.
The 0s do NOT show us the preciseness of this
measurement. The 0s are simply place holders.
9800 has three significant digits. The digits 9 and 8
are significant because they are non-zero digits. The
0s are NOT significant because they are in the whole
number part of this number and are to the right of
significant digits.
TIP: Again, the 0s are included to show the value (i.e.
how large) the number (measurement) is. The 0s do
NOT show us the preciseness of this measurement.
The 0s are simply place holders.
A zero digit with a dot
underneath the zero is
significant.
950Ọ00
Tutoring and Learning Centre, George Brown College 2014
www.georgebrown.ca/tlc
This number has four significant digits. The digits 9
and 5 are significant because they are non-zero
digits. The zero with the dot underneath is
significant. The zero between 5 and the 0 with the
dot underneath is also significant because it’s
located between two significant digits.
Practice Question:
1. For each measurement below state the number of significant digits it has.
a) 53.409
b) 1.20
c) 0.0038
d) 90000
e) 4307
f) 105000.0
g) 0.00809
Answer:
1. a) five
e) four
b) three
f) seven
c) two
g) three
d) one
2. Operations with Significant Digits
Operations with measurements can change the number of significant digits the final
answer has. The following rules should be followed when rounding the final answer to
the correct number of significant digits:
-
For adding and subtracting, round the final answer to the least number of
decimal places in the measurements being added or subtracted.
Note: If you are adding or subtracting whole numbers, round to the same number of
significant digits as the least precise measurement.
-
For multiplying and dividing, round the final answer to the least number of
significant digits in the measurements being multiplied or divided.
-
For multiple operations, perform the entire calculation carrying all the digits.
Then, determine the number of significant digits or decimal places at EACH step
(following the correct order of operations). It is helpful to underline the “extra”
decimal places or significant digits being carried to the next step. Round the final
answer to the same number of significant digits or decimal places as the least
precise component of the calculation..
Tutoring and Learning Centre, George Brown College 2014
www.georgebrown.ca/tlc
Examples:
1. Perform each calculation and round to the correct number of significant digits.
a) 14.578 + 34.2 =
b) 54.76 – 1.999 =
c) 58.31 ÷ 2.5 =
d) 0.054 x 19.3 =
32.09 + 1.2 −17.035
e)
=
19.8
Solutions:
1. a) 14.578 + 34.2 = 48.778
Round to one decimal place.
Final answer is 48.8
b) 54.76 – 1.999 = 52.761
Round to two decimal places.
Final answer is 52.76
c) 58.31 ÷ 2.5 = 23.324
Round to two significant digits.
Final answer is 23
d) 0.054 x 19.3 = 1.0422
Round to two significant digits.
Final answer is 1.0
e)
32.09 + 1.2 −17.035
19.8
=
Step 1: 32.09 + 1.2 = 33.29
The intermediate answer should have one decimal place.
Step 2: 33.29 – 17.035 = 16.255
The intermediate answer should have one decimal place.
Step 3: 16.255 ÷ 19.8 = 0.820959596…
The answer is rounded to three significant digits.
The final answer is 0.821.
Tutoring and Learning Centre, George Brown College 2014
www.georgebrown.ca/tlc
Practice Exercises:
1. Perform each calculation and round to the correct number of significant digits.
a) 87.654 + 123.9 =
b) 98.36 ÷ 5.8 =
c) 348.72 x 0.0506 =
d) 205.06 – 19.2 + 48.001 =
e) 78.32 ÷ 2.1 x 193 =
f) 90.3 x 1.2 + 5.84 =
g)
h)
73.2+18.72 x 6.1
123.45
5.1
3.4
=
+ 7.6 x 100.3 =
Answers:
1. a) 211.6
b) 17
c) 17.6
d) 233.9
e) 7200
f) 110
g) 55
h) 790
Tutoring and Learning Centre, George Brown College 2014
www.georgebrown.ca/tlc