Transcript Lesson 13a - Significant digits

SIGNIFICANT DIGITS
RULES FOR SIGNIFICANT DIGITS
1. Non-zero digits are ALWAYS significant.
Example- 123456789
2. Zeros that are between other significant digits are
ALWAYS significant.
Example- 3004
3. Final zeros that occur before or after the decimal are
ALWAYS significant.
Example- 78.00
4.
Zeros used for spacing the decimal are NOT
significant.
Example- 0.003
EXAMPLES
3 SIG FIGS
4 SIG FIGS
5 SIG FIGS
250 m/s
3150 m/s
74850 m/s
25.0 m/s
315.0 m/s
7485.0 m/s
2.50 m/s
31.50 m/s
748.50 m/s
0.250 ml
3.150 ml
74.850 ml
0.0250 ml
0.3150 ml
7.4850 ml
0.00250 ml
0.03150 ml
0.74850 ml
0.000250 ml
0.003150 ml
0.074850 ml
700 m/s
7 000 m/s
70 000 m/s
8.07 x 106 m/s
8.007 x 106 m/s
8.0007 x 106 m/s
HOW MANY SIGNIFICANT DIGITS?
2804
2.84
0.0029
4.6 X 104
75.00
50000
360
0.00305
30.24
6.89
0.001
6.0
123.056
100.04
ADDING & SUBTRACTING


When you have numbers to add/subtract you will sometimes
need your answer to have the correct number of significant
digits. Here is the rule:
Look at all of the numbers to add/subtract and find the
number with the LEAST number of sig. digs. AFTER the
decimal. This is how many sig. digs. should be after the
decimal in your answer.
Example 24.686
2.343
3.21
30.239
ANSWER = 30.24
MULTIPLYING & DIVIDING


When you have numbers to multiply/divide you will
sometimes need your answer to have the correct number
of significant digits. Here is the rule:
Look at all of the numbers to multiply/divide and find the
number with the LEAST number of sig. digs. This is how
many sig. digs. that you should have in your answer.
Example - 3.22 x 2.1 = 6.762
ANSWER = 6.8
EXAMPLE PROBLEMS FOR +/•
1.2 + 1.26 =
•
2.46
•
•
2.476-1.72 =
•
0.756
•
•
Final Answer: 2.5
Final Answer: 0.76
10.72694321 – 10.1 =
•
0.62694321
•
Final Answer: 0.6
EXAMPLE PROBLEMS FOR X/÷
•
1.53 x 2.5
•
3.825
•
•
10.0 / 5.0 =
•
2
•
•
Final Answer: 3.8
Final Answer: 2.0
10.2 x 1000
•
102,000
•
Final Answer: 10.2 x 10³