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Significant Figures The Four Rules

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**Rule #1: All non-zero numbers are always…**

SIGNIFICANT!!! 4 3 6 9 2 7 8 1 5

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**So, the only number to worry about is…**

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**Using Othello to understand Rule #2**

Zeros between non-zero numbers are always significant

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**Using Othello to understand Rule #2**

Zeros between non-zero numbers are always significant

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**The Other Zero Rules Rule #3:**

All final zeros to the ______ of a decimal point are significant. right Rule #4: Zeros that act as ____________ are NOT significant. placeholders

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**For rule #3 and #4, it can be summarized by these two questions:**

1) Is there a decimal point? 2) Is there a number in front of the zero? Answering yes to both of these questions means that the zeros are significant figures.

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Significant? .0

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Another note: if a number is written in scientific notation, all numbers before the x 10 are significant, all numbers after are not significant.

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Is It Significant?

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**16407.100 0.00010080 904008000 Significant Non-Significant 8 sig figs**

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**Let’s look at some examples**

a L b L c x 105 kg d kg 4 significant figures 7 significant figures 5 significant figures 3 significant figures

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**Let’s look at some examples**

a s b mL c x 10-8 g d mL 5 significant figures 3 significant figures 5 significant figures 2 significant figures

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**So, why are significant figures important?**

Significant figures and math

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**Addition and Subtraction**

When adding or subtracting—the answer has the least number of decimal places Hint: Before adding and subtracting, line up all the numbers so the decimal points align. 187.6 961.95 18.95 189.9 19

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**Multiplication and Division**

When multiplying or dividing—the product has the least number of significant figures 21.6 x (3 sig figs) 7216 ÷ (4 sig figs) (2 sig figs) (2 sig figs) 1.4472 (2 sig figs) (2 sig figs) 1.4 210000 Or 2.1 x 105

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**Now, try some of these on your own**

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**Addition a) 43.2 cm 51.0 cm + 48.7 cm b) 258.3 kg 257.1 1 kg + 253 kg**

c) mg mg mg kg mg 142.9 cm 768 kg mg

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**Multiplication a) 24 m x 3.26 m = 78.24 m = 78 m b) 120 m x 0.10 m**

c) 1.23 m x 2.0 m = 2.46 m = 2.5 m d) 53.0 m x 1.53 m = m = 81.1 m

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Why do we have them? When we measure things, we want to measure to the place we are sure of and guess one more space.

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**So, they show the uncertainty in our measurements**

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Since the marks on this ruler are subdivided as they are, our answer for the length of this nail has 3 significant figures.

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However, we only have significant figures when we are measuring something. Counting will give you an exact number.

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