Significant Figure Rules RulesExamples The following are always significant Non zero digits Zeros...
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Transcript of Significant Figure Rules RulesExamples The following are always significant Non zero digits Zeros...
![Page 1: Significant Figure Rules RulesExamples The following are always significant Non zero digits Zeros between non zero digits Zero to the right of a non zero.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649f505503460f94c72f36/html5/thumbnails/1.jpg)
![Page 2: Significant Figure Rules RulesExamples The following are always significant Non zero digits Zeros between non zero digits Zero to the right of a non zero.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649f505503460f94c72f36/html5/thumbnails/2.jpg)
Significant Figure Rules
Rules Examples
The following are always significant•Non zero digits•Zeros between non zero digits•Zero to the right of a non zero digit and to the left of a written decimal•Finishing zeros to the right of a decimal place
673 has 3
506 has 3
1.009 has 4
57.00 has 4
The following are NEVER significant•Zeros to the left of the first non zero digit
0.67 has 20.004 has 1
EXCEPTIONS•Counting numbers•Exact conversion factors
30 days in June100 cm in 1 m
![Page 3: Significant Figure Rules RulesExamples The following are always significant Non zero digits Zeros between non zero digits Zero to the right of a non zero.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649f505503460f94c72f36/html5/thumbnails/3.jpg)
Math in Significant Figures
• Multiplication and Division– The # of significant figures in the
result is the same as the # in the least precise measurement used in the calculation
– 0.024 x 1244= (two significant figures )
• Sample Problem: Find the area of a rectangle 2.1 cm by 3.24 cm.– Solution: Area = 2.1 cm x 3.24 cm = 6.8cm2
![Page 4: Significant Figure Rules RulesExamples The following are always significant Non zero digits Zeros between non zero digits Zero to the right of a non zero.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649f505503460f94c72f36/html5/thumbnails/4.jpg)
Math in Significant Figures
• Addition and Subtraction– The # of significant figures in the result has the same
number of decimal places as the least precise measurement
– Round to the least # of decimal places• Sample Problem: Add 42.56 g + 39.460 g + 4.1g
Solution:42.56 g
39.460 g4.1 g
Sum = 86.1 g
![Page 5: Significant Figure Rules RulesExamples The following are always significant Non zero digits Zeros between non zero digits Zero to the right of a non zero.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649f505503460f94c72f36/html5/thumbnails/5.jpg)
Rules for Rounding
• In a series of calculations, carry the extra digits through to the final result, then round
• If the digit to be removed– Is less than 5, the preceding digit
stays the same– Is equal to or greater than 5, the
preceding digit is increased by 1
![Page 6: Significant Figure Rules RulesExamples The following are always significant Non zero digits Zeros between non zero digits Zero to the right of a non zero.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649f505503460f94c72f36/html5/thumbnails/6.jpg)
Scientific Notation
![Page 7: Significant Figure Rules RulesExamples The following are always significant Non zero digits Zeros between non zero digits Zero to the right of a non zero.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649f505503460f94c72f36/html5/thumbnails/7.jpg)
![Page 8: Significant Figure Rules RulesExamples The following are always significant Non zero digits Zeros between non zero digits Zero to the right of a non zero.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649f505503460f94c72f36/html5/thumbnails/8.jpg)
Why use Scientific Notation?
M x 10n
• M is a number between 1 and 10• n is an integer• all digits in M are significant
– if n = (+)#, then move the decimal to the right
• 1.0 x 105 = 100000
– If n = (-)#, then move the decimal to the left
• 1.0 x 10-5 = .00005
![Page 9: Significant Figure Rules RulesExamples The following are always significant Non zero digits Zeros between non zero digits Zero to the right of a non zero.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649f505503460f94c72f36/html5/thumbnails/9.jpg)
Sample Problems
• Express these numbers in decimal notation.
1. 8.32 x 10-2 _____________
2. 5.4 x 104 ______________
3. 9.67 x 103 _____________
4. 1.457 x 102_____________
5. 3.00 x 10-1 _____________
6. 2.22 x 10-6 _____________
![Page 10: Significant Figure Rules RulesExamples The following are always significant Non zero digits Zeros between non zero digits Zero to the right of a non zero.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649f505503460f94c72f36/html5/thumbnails/10.jpg)
Reducing to Scientific Notation
1. Move decimal so that M is between 1 and 10
2. Determine n by counting the number of places the decimal point was moved
a. Moved to the left, n is positive
b. Moved to the right, n is negative
![Page 11: Significant Figure Rules RulesExamples The following are always significant Non zero digits Zeros between non zero digits Zero to the right of a non zero.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649f505503460f94c72f36/html5/thumbnails/11.jpg)
Sample Problems
• 47,000 _____________________
• 0.00047 ____________________
• 0.4100 _____________________
• 421 _______________________
• 5630 _______________________
![Page 12: Significant Figure Rules RulesExamples The following are always significant Non zero digits Zeros between non zero digits Zero to the right of a non zero.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649f505503460f94c72f36/html5/thumbnails/12.jpg)
Mathematical Problems
• Addition and subtraction– Operations can only be performed if the
exponent on each number is the same
• Multiplication– M factors are multiplied– Exponents are added
• Division– M factors are divided– Exponents are subtracted (numerator -
denominator)
![Page 13: Significant Figure Rules RulesExamples The following are always significant Non zero digits Zeros between non zero digits Zero to the right of a non zero.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649f505503460f94c72f36/html5/thumbnails/13.jpg)
Sample Problems
1. (2.8 x 10 5) +(7.53 x 10 5)________________________
2. (3.1 x 10 -2) (4.380 x 10 3)________________________
3. (4.20 x 10 2) (0.040 x 10 -1)________________________
4. 3.0 x 10 3 ÷ 1.2 x 10 4 ________________________
5. 4.95 x 10 6 ÷ 2.33 x 10 -2 ________________________