11Mr. Shields Regents Chemistry U00 L02

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Significant Figures

In all numbers there are digits that are Significant& others are not Significant.

Why should we be concerned which numbers are significant?

1) Measurements are never exact.

2) Scientist want to record their data (nos.) with the LEAST AMOUNT OF UNCERTAINTY.

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Significant Figures

Scientists created rules so numbers could be written with the least amount of uncertainty. These are the rules governing what are called Significant figures.

By using these rules scientist can be confident that the numbers people report don’t exaggerate their accuracy!

The greater the number of significant figures the morePRECISE the number

For example 3.41 is less precise than 3.413341 There are more sig figs in the 2nd number

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Significant Figures

To determine the number of significant figures in a numberLet’s take a look a technique that will help us figure it out

It’s called the ATLANTIC - PACIFIC RULE

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Atlantic – Pacific Rule1. Draw a map of the United States and label the 2 oceans … which are???

 

PACIFICATLANTIC

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Atlantic – Pacific Rule1. If a decimal point is Present in the number

start counting from the Pacific side

2. If a decimal point is Absent in the number count from the Atlantic side

3. Begin counting all numbers from the first NON-ZERO digit

- That number and all digits after it (including zeros) are SIGNIFICANT

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0.06901

100,100,300

Try the rule with these two numbers. How manySig figs are there?

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Significant Figures

Lastly, all COUNTING and DEFINED NUMBERS aretreated as if they have an INFINITE no. of Sig Figs Ex: 2 pairs of gloves Counting (infinite sig fig)

7 Keys Counting “

2.54 cm = 1 inch Definition “

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Atlantic – Pacific Rule

Let’s try some examples. How many significantFigures are in the following numbers?

3456 4 sig figs

0.040860 5 sig figs

3.50001 6 sig figs

20000 1 sig fig

7 oranges Infinite sig figs

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Atlantic – Pacific Rule

Let’s try some more examples. How many sig figsAre there in the following pairs of numbers?

750 vs. 750. 2 vs 3 sig figs

1001 vs. 1000 4 vs. 1 sig figs

2.07 vs. 2.070 3 vs. 4 sig figs

0.00572 vs 572 3 vs. 3 sig figs

1001. vs. 1000. 4 vs 4 sig figs

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Working with Significant Figures

It’s important we know how to manipulate Significant figures. We’ll need to know the same manipulations we needed to know for Scientific Notation, namely:

1. Addition +

3. Multiplication x

4. Division /

2. Subtraction -

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Working with Significant Figures

Let’s look at the rules that govern these mathematical operations.

1 & 2. Addition & Subtraction have the same rule

The number of decimal places in the Ans. EQUALS the Smallest Number of DECIMAL places in any of the nos.Being added or subtracted.

Ex: 6.8 + 11.934 = 18.734 = 18.7

2.01 + 0.003 + 1 = 3.013 = 3

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Working with Significant Figures

3 & 4. Multiplication & Division have the same rule

The number of sig figs in the ans. Equals the number ofSig Figs in the least precise number

Ex: 6.8 x 11.934 = 81.1512 = 81.

2.014 / 0.70 = 2.877143 = 2.9