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Significant Figures

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**Why do we need to know significant figures?**

We as scientists need to measure things as we perform experiments. Instruments have different degrees of precision We measure to the last known calibration, and estimate the unknown.

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The Rules

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**Significant Figures – The Rules**

1. Nonzero numbers 1 – 9 are always significant. Examples: 1 meter sig fig 92 liters sig figs 34578 grams sig figs

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**Significant Figures – The Rules**

2. Imbedded zeros (zeros between nonzero numbers) are always significant. Examples: 202 cm 3 sig figs 10509 mL 5 sig figs 2039 kg 4 sig figs 90009 g 5 sig figs

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**Significant Figures – The Rules**

3. Leading zeros are never significant. 4. Trailing zeros after a nonzero number after the decimal are significant. Examples: g 3 sig figs mm 4 sig figs L 3 sig figs

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**Significant Figures – The Rules**

5. Trailing zeros before the decimal are significant only if the decimal point is specified. Examples: 100. dg 3 sig figs 100 dg 1 sig fig 8900 km 2 sig figs 8900. km 4 sig figs

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Exact Numbers An exact number is a number that cannot be changed. (Cannot be halved or split up) Ex. 2 atoms, 1 proton, a hundred dollar bill We include most conversion factors as exact numbers Ex. 1m = 100 cm When you work with exact numbers, you consider them to have infinite sig figs. (You don’t have to worry about them!)

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**0.00770800 RECAP #1 Leading Zeros Imbedded Zero after the decimal**

Nonzero numbers Trailing Zeros after the decimal

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6 significant figures

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**22060 RECAP #2 (none) Nonzero numbers Trailing zero with no decimal**

Leading Zeros Imbedded Zero (none) 22060 Nonzero numbers Trailing zero with no decimal

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4 significant figures

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Lets Practice!

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56 meters 2 sig figs Rule 1

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20 grams 1 sig fig Rule 1, 5

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303.0 mL 4 sig figs Rule 1, 2, 4

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200 kilograms 1 sig fig Rule 1, 5

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207 kilometers 3 sig figs Rule 1,2

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grams 4 sig figs Rule 1,3,4

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m 5 sig figs Rule 1,2,3,4

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km 3 sig figs Rule 1,2,5

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1.10 x 102 hm 3 sig figs Rule 1, 4

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2.2 x 1034 atoms infinite sig figs

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Rounding Numbers If you have to round and the number you are looking to round is less than 5, don’t round. Example: 214 round to 2 s.f. Answer = 210

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Rounding Numbers If you have to round and the number you are looking to round is 5 or greater, round up. Example: 215 round to 2 s.f. Answer = 220

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**Adding and subtracting with significant figures.**

When adding or subtracting significant figures, you round your answer to the least number of places after the decimal that are contained in your problem.

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**YOU ARE LOOKING AT PLACES AFTER THE DECIMAL NOT SIGNIFICANT FIGURES!**

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Example: = 6.0 You look for the least number of PLACES after the decimal. 2.00 = 2 places after the decimal 4.0 = 1 place after the decimal Your answer can only have one place after the decimal.

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**2.0 + 4 = 6 Example: 2.0 = 1 place after the decimal**

4 = no places after the decimal Your answer can not have any places after the decimal.

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Example: – = =0.055 = 5 places after the decimal 0.001 = 3 places after the decimal Your answer can only have 3 places after the decimal.

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Let’s Practice 17.0 – = Answer 16.5

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= Answer 56

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100.0 – = 28.48 Answer 28.5

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= Answer 20

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**Multiplying and Dividing with Significant Figures**

When multiplying or dividing with significant figures, your answer must be rounded to the least number of significant figures in the problem.

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**YOU ARE LOOKING AT SIGNIFICANT FIGURES NOT PLACES AFTER THE DECIMAL!**

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Example 20.0 x = 284.4 Answer 284

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430 x = 1.29 Answer 1

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2020 x = Answer 1.60 x 106

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50.0 / = 2500 Answer 2500

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50.0 / = 2500 Answer 2.50 x 103

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