Significant Figures.

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Presentation transcript:

Significant Figures

Why should we be concerned which numbers are significant? 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.

It’s called the ATLANTIC - PACIFIC RULE Significant Figures To determine the number of significant figures in a number let’s take a look a technique that will help us figure it out It’s called the ATLANTIC - PACIFIC RULE

Atlantic – Pacific Rule 1. Draw a map of the United States label the 2 oceans … which are??? PACIFIC ATLANTIC

Atlantic – Pacific Rule If a decimal point is Present in the number start counting from the Pacific side (Left Side) 2. If a decimal point is Absent in the number count from the Atlantic side (Right Side) 3. Begin counting all numbers from the first NON-ZERO digit - That number and all digits after it (including zeros) are SIGNIFICANT

Atlantic – Pacific Rule Let’s try some examples. How many significant Figures are in the following numbers? 4 sig figs 3456 0.040860 5 sig figs 3.50001 6 sig figs 1 sig fig 20000 7 oranges Infinite sig figs

Atlantic – Pacific Rule Let’s try some more examples. How many sig figs Are there in the following pairs of numbers? 750 vs. 750. 2 vs 3 sig figs 4 vs. 1 sig figs 1001 vs. 1000 3 vs. 4 sig figs 2.07 vs. 2.070 0.00572 vs 572 3 vs. 3 sig figs 1001. vs. 1000. 4 vs 4 sig figs

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 + 2. Subtraction - 3. Multiplication x 4. Division /

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 Answer 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

Working with Significant Figures 3 & 4. Multiplication & Division have the same rule The number of sig figs in the answer Equals the number of Sig Figs in the least precise number Ex: 6.8 x 11.934 = 81.1512 = 81. 2.014 / 0.70 = 2.877143 = 2.9