Significant
figures and calculation and rules for counting significant figures

1-
Nonzero integers are significant figures.

1.34 has 3
significant Figures (S.F.).

2.3456 have 5 S.F.

2-
Zeros are three classes:

A - Leading zeros that precede all
nonzero are not significant figures Example: 0.0025 has 2 S.F.

B - Captive zero (between nonzero)
are significant figures Example: 1.008 has 4 S.F.

C - Trailing zero at the right end

If the number contains decimal
point are significant figures Example: 100 have 1 S.F.

1.00x102 has 3 S.F.

100. has 3 S.F.

0.003020200 has 7 S.F.

3-
Exact number obtained by counting or definition assumed to have infinite number
of significant figures.

Examples

1-
3 apples have ꝏ S.F.

2-
8 molecules have ꝏ S.F.

3-
Circumference of circle= 2πr

4-
1 in= 2.54 cm

Exponential notation (also called
scientific notation) used to:

1- Determine number of significant
figures

2- Write very large or very small
number (example: speed of light= 3.00 x 108)

A x 10n: where 1 < or = A < 10

Example:

0.000060 = 6.0 x 105

4.340x10-4 = 0.0004340

Example
1.3

A - 0.0105 g 3 significant numbers

B - 0.050080 5 significant numbers

C - 8.050x10-3 4 significant numbers

Rules
for significant figures in Mathematical operations

1-
For multiplication and division: number of significant figures in
the result is the same as the number of significant figures in the least
precise measurement used in calculation.

Example:
4.56
x 1.4 = 6.38 rounded to 6.4 (2 S.F.)

2-
For addition or subtraction: the result has the same number of decimal
places as the least precise measurement.

Example:

12.11

+ 18.0 ← Limiting term has one decimal place

+ 1.013

31.123 corrected to 31.1 ← one decimal place

Rules
for Rounding

1- In a series of calculation carry
out the extra digits through to the final result then round.

2- If digit to be removed :

a. is less than 5, the preceding digit stays the same.

For example, 1.33 rounds to
1.3.

b. is equal to or greater than 5, the preceding digit is increased by 1. For
example, 1.36
rounds to 1.4.

Although rounding is generally
straightforward, one point requires special emphasis.

As an illustration, suppose that
the number 4.348 needs to be rounded to two significant figures. In doing this,
we look only at the first number to the right of the 3:

4.348

Look
at this number to

round
to two significant figures.

The number is rounded to 4.3
because 4 is less than 5. It is incorrect to round sequentially.

For example, do not round the 4 to
5 to give 4.35 and then round the 3 to 4 to give 4.4.

When rounding, use
only the first number to the right of the last significant figure.

Examples:

A - 1.05x10-3 ÷
6.135 = 1.71149x10-4 =
the answer is 1.71x10-4

B- 21 – 13.8 = 7.2 the answer is 7