Significant Figures

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.

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

Significant Figures It’s called the ATLANTIC - PACIFIC RULE 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 and 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 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

0.06901 100,100,300 Try the rule with these two numbers. How many Sig figs are there? 0.06901 100,100,300

Significant Figures Lastly, all COUNTING and DEFINED NUMBERS are treated 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 “

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 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

Working with Significant Figures 3 & 4. Multiplication & Division have the same rule The number of sig figs in the ans. 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