the significant figures in a measurement consist of all the digits known with certainty plus one...
TRANSCRIPT
![Page 1: The significant figures in a measurement Consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated. What](https://reader035.vdocument.in/reader035/viewer/2022062805/5697c0121a28abf838ccc36b/html5/thumbnails/1.jpg)
![Page 2: The significant figures in a measurement Consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated. What](https://reader035.vdocument.in/reader035/viewer/2022062805/5697c0121a28abf838ccc36b/html5/thumbnails/2.jpg)
The significant figures in a measurementConsist of all the digits known with certainty plus one final digit, which is uncertain or is estimated.
What are Significant Figures?
![Page 3: The significant figures in a measurement Consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated. What](https://reader035.vdocument.in/reader035/viewer/2022062805/5697c0121a28abf838ccc36b/html5/thumbnails/3.jpg)
CERTAIN VALUE: 75UNCERTAIN VALUE: 0.99~1.1
Your reading might be 76 ml. But, how sure are you that it is really 76 ml? Is it possible that it’s also 75.99 or 76.01?
![Page 4: The significant figures in a measurement Consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated. What](https://reader035.vdocument.in/reader035/viewer/2022062805/5697c0121a28abf838ccc36b/html5/thumbnails/4.jpg)
•All measurements are approximations—no measuring device can give perfect measurements without experimental uncertainty. By convention, a mass measured to 13.2 g is said to have an absolute uncertainty of plus or minus 0.1 g and is said to have been measured to the nearest 0.1 g. In other words, we are somewhat uncertain about that last digit—it could be a "2"; then again, it could be a "1" or a "3". A mass of 13.20 g indicates an absolute uncertainty of plus or minus 0.01 g.
![Page 5: The significant figures in a measurement Consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated. What](https://reader035.vdocument.in/reader035/viewer/2022062805/5697c0121a28abf838ccc36b/html5/thumbnails/5.jpg)
1 2 3 4 5 6 7
Measurements are always all measured values plus one approximated value. The pencil is 3.6 cm long.
3 4
With more calibration a more precise measurement is possible The pencil is 3.64 cm long!
3.6 3.7
Now 3.640 cm !The calibration of the instrumentdetermines measurement precision
![Page 6: The significant figures in a measurement Consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated. What](https://reader035.vdocument.in/reader035/viewer/2022062805/5697c0121a28abf838ccc36b/html5/thumbnails/6.jpg)
![Page 7: The significant figures in a measurement Consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated. What](https://reader035.vdocument.in/reader035/viewer/2022062805/5697c0121a28abf838ccc36b/html5/thumbnails/7.jpg)
What is Accuracy?•Accuracy - a measure of how close
a measurement is to the true value of the quantity being measured.
►Who is more accurate when measuring a book that has a true length of 17.0cm?
• Andrea:• 17.0cm, 16.0cm, 18.0cm, 15.0cm• Amy: • 15.5cm, 15.0cm, 15.2cm, 15.3cm
![Page 8: The significant figures in a measurement Consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated. What](https://reader035.vdocument.in/reader035/viewer/2022062805/5697c0121a28abf838ccc36b/html5/thumbnails/8.jpg)
What is Precision?
• Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is.
• ►Who is more precise when measuring the same 17.0cm book?
• Andrea:• 17.0cm, 16.0cm, 18.0cm, 15.0cm• Amy: • 15.5cm, 15.0cm, 15.2cm, 15.3cm
![Page 9: The significant figures in a measurement Consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated. What](https://reader035.vdocument.in/reader035/viewer/2022062805/5697c0121a28abf838ccc36b/html5/thumbnails/9.jpg)
Rules For Significant Figures
1. Significant figures are used for measured numbers and for numbers derived from measurements; does not include
definitions (ex. 1000ml=1L) or counting numbers (ex. 1,2,3 etc)
10 mm = 1cm = (2 significant figures)100cm = 1m = (3 significant figures)1000g = 1kg= (4 significant digits)
![Page 10: The significant figures in a measurement Consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated. What](https://reader035.vdocument.in/reader035/viewer/2022062805/5697c0121a28abf838ccc36b/html5/thumbnails/10.jpg)
2. Digits from 1-9 are always significant.
Ex. 2342 = 4 significant figures 25 = 2 significant figures 23.42 = 4 significant figures
![Page 11: The significant figures in a measurement Consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated. What](https://reader035.vdocument.in/reader035/viewer/2022062805/5697c0121a28abf838ccc36b/html5/thumbnails/11.jpg)
3. Zeros between two other significant digits are always significant.Ex. 5 055 g = 4 significant figures
207 ml = 3 significant figures
![Page 12: The significant figures in a measurement Consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated. What](https://reader035.vdocument.in/reader035/viewer/2022062805/5697c0121a28abf838ccc36b/html5/thumbnails/12.jpg)
4. One or more additional zeros to the right of both the decimal place and another significant digit are significant.
•Ex. 5.00 = 3 significant figures 50.05 = 4 significant figures 50.50 = 4 significant figures
![Page 13: The significant figures in a measurement Consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated. What](https://reader035.vdocument.in/reader035/viewer/2022062805/5697c0121a28abf838ccc36b/html5/thumbnails/13.jpg)
5. Zeros used solely for spacing the decimal point (placeholders) are not significant.
Ex. 0.007 (1 significant figure) 1000 ( 1 significant figure)
0.015 ( 2 significant figures)
![Page 14: The significant figures in a measurement Consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated. What](https://reader035.vdocument.in/reader035/viewer/2022062805/5697c0121a28abf838ccc36b/html5/thumbnails/14.jpg)
6. Exact numbers have an infinite number of significant digits but they are generally not reported. All non zero digits are significant.
Ex. 2 ( 1 significant figure) 453 (3 significant figures)
![Page 15: The significant figures in a measurement Consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated. What](https://reader035.vdocument.in/reader035/viewer/2022062805/5697c0121a28abf838ccc36b/html5/thumbnails/15.jpg)
Exact equivalences have an unlimited number of significant figures
There are exactly 3 feet in exactly 1 yard. Therefore the 3 can be 3 or 3.0 or 3.00 or 3.000 etc. and the 1can be 1 or 1.0 or 1.00 or 1.000 etc. !
The same is true for:
![Page 16: The significant figures in a measurement Consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated. What](https://reader035.vdocument.in/reader035/viewer/2022062805/5697c0121a28abf838ccc36b/html5/thumbnails/16.jpg)
SUMMARYEXAMPLES # OF SIG.
FIGRules
453 kg 3All non-zero digits are always significant.
5057 L 4Zeros between 2 sig. dig. are significant.
5.00 g 3Additional zeros to the right of decimal and a sig. digits are significant.
0.007 ml 1 Placeholders are not sig.
0.02300 ml 4Zeros to the right of the decimal and to the right of non zeros are significant.
![Page 17: The significant figures in a measurement Consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated. What](https://reader035.vdocument.in/reader035/viewer/2022062805/5697c0121a28abf838ccc36b/html5/thumbnails/17.jpg)
It’s Your Turn To Try!
•How many significant figures do the following numbers have?
![Page 18: The significant figures in a measurement Consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated. What](https://reader035.vdocument.in/reader035/viewer/2022062805/5697c0121a28abf838ccc36b/html5/thumbnails/18.jpg)
1) 1234 _____2) 0.023 _____3) 890 _____4) 91010 _____5) 9010.0 _____6) 1090.0010 _____7) 0.00120 _____8) 0.00030 _____9) 1020010 _____10) 72 _____11) 1000 _____12) 918.010 _____13) 0.0001 _____14) 0.00390 _____15) 8120 _____
1.) 42.) 23.) 24.) 45.) 56.) 87.) 38.) 29.) 610.)211.) 112.) 613.) 114.) 315.) 3
![Page 19: The significant figures in a measurement Consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated. What](https://reader035.vdocument.in/reader035/viewer/2022062805/5697c0121a28abf838ccc36b/html5/thumbnails/19.jpg)
ASSIGNMENT:
Determine the number of significant digits in the following numbers.1) 5600 _____2) 45.00_____3) 105.0_____4) 0.00565_____5) 0.005400_____6) 89.543_____7) 5, 056, 300_____8) 95.0540_____9) 93, 000, 000_____10) 21.35_____
![Page 20: The significant figures in a measurement Consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated. What](https://reader035.vdocument.in/reader035/viewer/2022062805/5697c0121a28abf838ccc36b/html5/thumbnails/20.jpg)