Significant Figures

Rules1. All nonzeroes are significant2. Zeroes in-between are significant3. Zeroes to the left are not significant4. Zeroes to the right are not significant

unless they follow a decimal.5. All numbers in scientific notation are

significant6. Exact numbers are obtained by

counting or by using definitions such as 1 in = 2.54 cm, and are considered infinite in significance

Adding and Subtracting• Always use the least significant decimal place.• example:• 1253.747 + 1.1 = 1254.8

1253.757 + 1.1

= 1254.9 round up

.0365578 - .00223 =.03433 or 3.433 X 10-2

Multiplying and Dividing• All ways go by the least number of

significant figures. examples:

1253.747 X 1.1 =1379.1217 No

=1400 or 1.4 x 103

Combining the math

• 55.657 -55.654 X .033 =

4.54

• 2 x 10-5

• Note the level of significance produced by the subtraction operation in the

numerator.

Logs    The logarithm (base 10) of x, log x = a, where x = 10a.

   The antilogarithm (base 10) of a, antilog a = x, where x = 10a.

   A logarithm is divided into two (2) parts by the decimal.  The integer before the decimal is the characteristic and the numbers after the decimal are the mantissa.

   If a number is a logarithm, since the characteristic reflects the power of 10, i.e. the exponent, it is not considered to be part of the significant figures.  Only the digits in the mantissa (after the decimal) are significant.

AntilogAntilogSig Figs

LogLog

Sig Figs

567(5.67 X 102)

3 2.754 3

0.0025(2.5 X 10-3)

2 -2.60 2

205.203(2.05203 X 102)

6 2.312183 6

3.400 X 1020 4 20.5315 4

0.0000002(2 X 10-7)

1 -6.7 1

Exact Numbers

• 1 dozen eggs

• 25 students

• 2.54 cm = 1 in

• 6.02213 x 1023 NOT