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Determining Number of Significant Figures in Answer
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When you do calculations, you can only be as exact as the numbers you start with.
There are different rules for how exact you can be depending on whether you're
1) multiplying and dividing, or
2) adding and subtracting.

To decide how many sig figs are allowed in the answer when multiplying or dividing:
1) Multiply or divide the numbers.
2) Count the number of sig figs in each number.
3) The answer is allowed as many sig figs as the least number of sig figs in the numbers you began with, since you can only be as accurate as the least accurate measurement.
4) Round your answer so that it has that many sig figs.

Example 1: Sig Figs for 45,000 x .07324.
Step 1:  Enter the numbers in your calculator. 45,000 x .07324 = 3295.8
Step 2:  Count the sig figs in each number. 45,000 has two sig figs and .0732 has three sig figs.
45,000   x .07324   = 3295.8
    
     
       
           
2 sig figs
4 sig figs
Who cares!
Four doesn't matter
because it's higher than 2.
Answer is only allowed two sig figs because this is the lowest number.

Step 3:  Count two digits from the left and draw a line. 32|95.8
Step 4:  Round to that number. 3300
final answer

Example 2:
Sig Figs for 1,802,700 divide 2.10.
Step 1:  Enter the numbers in your calculator. 1,802,700 divide 2.10 = 858,428.5714
Step 2:  Count the sig figs in each number. 1,802,700 has five sig figs and 2.10 has three sig figs.
1,805,100    divide  2.10   = 858,428.5714

      
     
           
Who cares!
Five doesn't matter
because it's higher than 3.
5 sig figs
3 sig figs
Answer is only allowed three sig figs because this is the lowest number.

                                                                                         
Step 3:  Count three digits from the left and draw a line. 858,|428.5714
Step 4:  Round to that number. 858,000
final answer


To decide how many "sig figs" are allowed in the answer when adding or subtracting:

1) Line up the numbers as though about to add or subtract (decimals must be lined up).
2) Draw a vertical line where the sig figs stop in each number.
3) Add or subtract the numbers.
4) Moving left to right, the sig figs in the answer must stop at the first line.
5) Round your answer to that place value.

Example 1: Sig Figs for 5.02 + 63
Step 1: Line up the numbers to add.
Step 2: Draw vertical lines where the sig figs stop in each number.
Step 3: Add the numbers.
Step 4: Sig figs in answer must stop
             at the first line.         
           
Step 5: Round answer to ones place.                                                68


Example 2: Sig Figs for 300 - 6070
Step 1: Line up the numbers to subtract.
Step 2: Moving left to right, draw vertical lines where the sig figs stop in each number.
Step 3: Subtract the numbers.
Step 4: Sig figs in answer must stop
             at the first line, moving left
             to right.
Step 5: Round answer to hundreds
             place.            
5800

Note: Using the rules for sig figs, it's possible to add or subtract two numbers and end up with the same number you started with.

This happens when the second number is too small to "make a dent in" the larger number.

Example 3: Adding 1 to 93,000,000
The earth is often said to be 93,000,000 (93 million) miles from the sun. This is not exact. It's rounded to the nearest million.
So it makes no sense to say, "If the earth moved 1 mile farther away, it would be 93,000,001 miles away."
Because we rounded to millions to begin with, if the earth moved 1 mile farther away, we'd have to say that it would still be 93,000,000 miles away.
In other words, adding the 1 didn't change anything because compared to 93 million, it's not significant.

Example 4: Add 5.3 and .0071955

                                                                     
So sig figs in the answer have to stop here,
because it's where the first line is.
                                     
So the answer is...
     5.3
The same number we started with!
(This won't happen often, but I point it out
because I don't want you to think you're
crazy if it does.)

People who saw this lesson also found the following lessons useful:
Significant Figures
Place Holder Zeroes
Significant Figures and Measurements
Scientific Notation and Significant Figures
Significant Figures and Conversion Factors
 
   
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