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# Zumdahl Chapter 1: Significant figures and calculation and rules for counting significant figures

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