Significant FiguresDigits Significant Figures When a scientist makes a measurement, he or she is allowed to estimate one digit. Consequently, the last digit of any measurement is always considered to be uncertain since it has been
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Significant Figures/Digits<br>
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Significant Figures When a scientist makes a measurement, he or she is allowed to estimate one digit.
Consequently, the last digit of any measurement is always considered to be uncertain since it has been estimated.<br>
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Significant Figures Significant digits (figures) include all
measured (certain) digits plus one estimated (uncertain) digit.<br>
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Significant Figures The precision of measurement is an important part of experimentation. Precision refers to the degree of exactness with which a measurement is made and stated. This precision is indicated by the number of significant digits in the measurement.<br>
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Significant Figures Accuracy is not the same thing as precision. Accuracy refers to how close to the accepted value a measurement is. We often show the accuracy of a measurement or calculation with % error.
Significant Figures How do you determine the number of significant digits in a measurement???
All nonzero digits are significant.<br>
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Significant Figures How do you determine the number of significant digits in a measurement???
2. A zero is significant if
It is the last digit to the right of a decimal.
It has a bar over it.
It is “sandwiched” between significant digits.<br>
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Significant Figures If a zero doesn’t fit into one of these 3 categories, it is merely a place-holder and hasn’t been measured or estimated so it isn’t significant.<br>
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Examples a) 86000 m ___
b) 200 g ___
90.08oC ___
200.0 g ___
0.00056 kg ___
70600 min ___ g) 2.00 s ___
h) 840 cars ___
i) 5000 cm ___
0.050 mL ___
5Ō00 cm ___
0.060700 mm ___<br>
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Significant Figures Rules for determining the number of significant figures in a calculated answer:
When multiplying or dividing, round your answer to the number of significant digits in the least precise measurement. This is called the weak unit.<br>
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Example 1 The answer to 4.54 cm x 6000 cm x 7.600 cm should contain _1_ significant figure
Why???<br>
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Example 1 (continued) The answer to…
2.00 g / (14.0 cm x 0.0606 cm x 0.0050 cm)
should contain _2_ significant figures.
Why?<br>
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Example 2 When adding and subtracting, round the answer to the largest place value containing an uncertain digit.
12.006 g 64.800 cm
.0050 g - 2.01 cm
+2500 g<br>
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Assignment Highlight all the significant digits
and give the number. 10 candles
0.010100 s
80 g
93000000 miles
150 mL
150.0 mL
0.0001 g
0.002000 Mm
1.0000 m<br>
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Assignment Round the following: 157 (to 2 sig figs)
16.5 (to 2 sig figs)
16950000 (to 3 sig figs)
0.0003361 (to 3 sig figs)
16.500001 (to 2 sig figs)
16949999 (to 3 sig figs)<br>
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Assignment Perform the following calculations rounding answers off to the correct number of sig figs:
Assume all are measurements
15.0 x 0.0002 x 653 = _________________________
(0.0340 x 1056) / 0.0020 = _____________________
24.000 + 3.1 + 1720.00 = ______________________
140002.00 – 15 = ____________________________
1500 – 0.00032 + 79.6610 = ____________________<br>
