8 Significant Figures

Significant figures The number of meaningful digits in a measurement including the uncertain digit. “sig figs” 0.520 0.0025 500 0.02300 120035 500. 2.0 x 105 3 do not count zeros at the beginning 2 1 do not count end zeros if no decimal 4 count all other zeros 6 3 2 do not expand

Significant figures The number of meaningful digits in 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 numbers that are counted or defined and not measured have zero uncertainty and 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 digits of 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 digits of 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 digits of any of the numbers used. 1. 21.036 + 22.1?? = 43.1 the 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 digits of 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 digits of any of the numbers used 2. 25.654 - 22.1?? = 3.6 the 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 digits of 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 digits of any of the numbers used 3. 301.2256 - 0.36 300.87 the 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 digits of 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 digits of 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 digits of 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 digits of 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 digits of 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 digits of any of the numbers used. 5. 2.463 x 10-5 0.00002463 + 5.006 x 10-2 0.05006 5.008 x 10-2 0.05008 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 digits of 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 digits of 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 digits of 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 2.657 x 10-12 2.657 x 10-14 0.02657 x 10-12 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 8.9967 x 1018 - 5.222 x 1015 0.005292 x 1018 - 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.