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Learn how to calculate significant figures, round answers correctly, and apply rules for adding and subtracting with precision. Explore examples and clear explanations for mastering this important concept in scientific measurement.
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8 Significant Figures
Significant figures The number of meaningful digitsin a measurement including the uncertain digit. “sig figs” 0.520 0.0025 500 0.02300 120035 500. 2.0 x 105 3 do not countzerosat the beginning 2 1do not count end zeros if no decimal 4count all other zeros 6 3 2do not expand
Significant figures The number of meaningful digitsin a measurement including the uncertain digit. “sig figs” 2.5002 0.00650 5001 0.0200300 0.02010 200 200. 2.0 x 102 2. x 102 5 3 4 6 4 1 3 2 1
Significant figures Exact numbersthat are counted or defined and not measured have zero uncertaintyand infinite “sig figs”. “sig figs” 2.50 cm 3 girls 62.33 kJ 1 cm = 10 mm 12.3 oC 200 lb 1 cm3 = 1 mL $75.00 3 infinite 4 infinite 3 1 infinite infinite
Adding and Subtraction with Significant Figures When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digitsof any of the numbers used. 1. 21.036 + 22.1
Adding and Subtraction with Significant Figures When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digitsof any of the numbers used 1. 21.036 + 22.1??
Adding and Subtraction with Significant Figures When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digitsof any of the numbers used. 1. 21.036 + 22.1?? = 43.1the largest decimal place is the first
Adding and Subtraction with Significant Figures When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digitsof any of the numbers used 2. 25.654 - 22.1?? =
Adding and Subtraction with Significant Figures When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digitsof any of the numbers used 2. 25.654 - 22.1?? = 3.6the largest decimal place is the first
Adding and Subtraction with Significant Figures When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digitsof any of the numbers used 3. 301.2256 - 0.36
Adding and Subtraction with Significant Figures When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digitsof any of the numbers used 3. 301.2256 - 0.36 300.87the largest decimal is the second
Adding and Subtraction with Significant Figures When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digitsof any of the numbers used 4. 8.053 x 107 + 2.3 x 104
Adding and Subtraction with Significant Figures When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digitsof any of the numbers used. 4. ↓largest decimal place 8.053 x 107 80530000. + 2.3 x 104 23000.
Adding and Subtraction with Significant Figures When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digitsof any of the numbers used. 4. ↓largest decimal place 8.053 x 107 80530000. + 2.3 x 104 23000. 8.055 x 107 80550000.
Adding and Subtraction with Significant Figures When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digitsof any of the numbers used. 5. 2.463 x 10-5 + 5.006 x 10-2
Adding and Subtraction with Significant Figures When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digitsof any of the numbers used. 5. 2.463 x 10-5 0.00002463 + 5.006 x 10-2 0.05006 ↑largest decimal place
Adding and Subtraction with Significant Figures When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digitsof any of the numbers used. 5. 2.463 x 10-5 0.00002463 + 5.006 x 10-2 0.05006 5.008 x 10-20.05008largest decimal place
Adding and Subtraction with Significant Figures When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digitsof any of the numbers used. 6. 5.331 x 10-4 - 2.126 x 10-5
Adding and Subtraction with Significant Figures When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digitsof any of the numbers used. 6. ↓largest decimal place 5.331 x 10-4 0.0005331 - 2.126 x 10-5 0.00002126
Adding and Subtraction with Significant Figures When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digitsof any of the numbers used. 6. ↓ largest decimal place 5.331 x 10-4 0.0005331 - 2.126 x 10-5 0.00002126 5.118 x 10-4 0.0005118
7. Add the two numbers- another way to do it 0.02657 x 10-12 2.657 x 10-12 2.657 x 10-14 0.027 x 10-12 2.684 x 10-12 Change the lower exponent to the higher and write it directly underneath. You are making the exponent larger so make the number smaller.
8. Subtract the two numbers- another way to do it 0.005292 x 1018 8.9967 x 1018 - 5.222 x 1015 - 0.0053 x 1018 8.9914 x 1018 Change the lower exponent to the higher and write it directly underneath. You are making the exponent larger so make the number smaller.
