1. 4.5678
600
0.5008
Significant Figures
1.004 8
32.000 7
2.45

2. Measurement always involves some estimating.
A better instrument allows for better measurements, recorded as a greater number of significant figures (digits).

3. Recording - include EVERY digit that is absolutely certain
Recording - include EVERY digit that is absolutely certain...PLUS the ONE digit that is estimated.
These are the SIGNIFICANT FIGURES.
3.2 3
estimated
certain

4. Rules for Significant Figures

5. 1. All non-zero digits are significant.
374 (3 sig figs) (2 sig figs)
2. All zeroes between non-zero digits are significant.
50407 (5 sig figs) (4 sig figs)
3. Leading zeroes are NOT significant.
0.54 (2 sig figs) (2 sig figs)

6. Always LOOK FOR A DECIMAL
4. Trailing zeroes are significant ONLY if there is a
decimal point.
2370 (3 sig figs) (2 sig figs)
160.0 (4 sig figs) (4 sig figs)

7. 6.02 x 10 23 Move the decimal so it is behind the first
To avoid confusion, scientists commonly use SCIENTIFIC NOTATION.
ALL digits in scientific notation are SIGNIFICANT
6.02 x 10 23
Move the decimal so it is behind the first
non-zero digit.
Count the number of places that you moved the
decimal - to the left is +, right is -

8. x 10 5
x 10 -3
1.5 x
6.35 x
103,000
1,236,000
42.0
1.03 x 10 5
1.236 x 10 6
4.20 x 10 1
2.1 x 10 -7
2.38 x 10 -4

9. 0-4: round down 5 -9: round up 0.00533 (2 sig figs) 0.0053
Rounding Rules
0-4: round down
5 -9: round up
(2 sig figs)
(3 sig figs) 426
1890 (1 sig fig) 2000
(2 sig figs) 0.030

10. Rules
for
Addition and Subtraction
Multiplication and Division

11. You can only give an answer that is as accurate as your least accurate number.

12. Add or subtract
Count digits to the right of the decimal.
Round the answer to match the value with the LEAST number of decimal places. =
Answer = 143.9
least number of decimal places

13. Multiply or divide
Answer is rounded to contain the same number of sig figs as the value with the LEAST.
51.3 × =
The answer, with significant figures, is 705.

14. DO NOT round for each calculation.
When performing multiple calculations, use the rule of the final calculation to round the answer.
( )(3.6) = ?
(0.5)(3.6) = 1.8
= 2
(0.5012)(3.6) =
= 1.8