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Significant Figure Calculations

Table of Contents
Introduction
Calculation Problems
Calculation Answers

     

     

Introduction

Multiplication and Division

Least Accurate Number - number with the fewest significant figures.  

The answer must have the same number of significant figures as the  least accurate number.

45,600 x 0.03100
----------------------
78.00 x 2341
   

      3               3
45,600 x 0.03100
---------------------- = 0.0077415963
78.00 x 2341
   4           4
   

45,600 and 0.03100 tie for least accurate number because each has 3 significant figures.

The rounded off answer is

0.00774

   First determine how many significant figures are in each  number.  I suggest you put the number of significant figures above or below each number.

   

Also multiply by ALL THE NUMBERS in the top and divide by ALL THE NUMBERS in the bottom to get the unrounded off value.

   

Identify the least accurate number.  It will have the fewest significant figures.

 

The answer must have the same number of significant figures as the least Accurate Number.

    

Addition and Subtraction

Least Accurate Number - Number with its last significant figure the least to the right.  After determining which digits are significant figures, the last significant figure is the significant figure the farthest to the right.  This is independent of the position of the decimal point.

The digits in GREEN are the last significant figures for the following numbers:

  
45800,  71000,  45.00,  0.00321,  0.092100
  

The answer must be rounded off to the same position compared to the decimal point as the least accurate number.

 47800
     532.10
+     84.1
--------------

   

 47800
     532.10
+     84.1
--------------
 48416.20

   

The answer is 48400

   First identify the last significant figure in each number.  I will identify by showing it in green.  I suggest you put an * above the last significant figure in each number.

  

Also calculate the unrounded off answer.

  

   

Identify the least accurate number by starting from the left.  It will be the first last significant figure you get to as you move from left to right.  The numbers must have their decimal points line up to use this process.  In this example it is the 8 in 47800.

Since the 8 is in the 3rd place to the left of the decimal point, the answer must have its last significant figure in the 3rd place to the left of the decimal point.  Observe that we are concerned with the position of the last significant figure not how many significant figures are present.

     

BE VERY CAREFUL TO MAKE A CLEAR DISTINCTION BETWEEN  HOW YOU ROUND OFF WITH MULTIPLICATION AND HOW YOU ROUND OFF WITH ADDITION !!!!  MULTIPLICATION IS ONLY CONCERNED WITH HOW MANY SIGNIFICANT FIGURES WHILE ADDITION IS ONLY CONCERNED WITH THE POSITION OF THE LAST SIGNIFICANT FIGURE.

    

Logarithms

 A logarithm has two parts.  The characteristic which are the digits only to the left of the decimal point.  The mantissa which are the digits only to the right of the decimal point.  All of the digits of the mantissa are significant figures.  None of the digits in the characteristic are significant.

The number and the logarithm must have the same number of significant figures.

Table of Contents

     

     

Calculation Problems

Correctly round off the following:
   
1. A. 42156 x 7800
--------------------- = ?
0.0500 x 3332

     
   

 C. 3420 x 60.00
-------------------- = ?
0.5411 x 8888
B. 0.0329 x 9830.0
----------------------- = ?
910.0 x 2278		 D. 98600 x 0.00004
----------------------- = ?
4297 x 3.654
    

   
   

     
2. A.       4870
    23134
  +      43.9
--------------

            
   

 C.       0.00340
      0.00212
  +  6.115
----------------
B.     0.006778
    0.0321
 + 0.00093
----------------
   		 D.       5411
          96.8
+   7250
---------------
   

   
3. A. log(64800) = ?
      		 C. antilog(3.211) = ?
B. log(4.211 x 10 -5) D. antilog( -6.33) = ?

Table of Contents

    

    

Calculation Answers

Correctly round off the following:
   
1. A. 42156 x 7800
--------------------- = ?
0.0500 x 3332		     5           2
42156 x 7800
--------------------- = ?
0.0500 x 3332
    3            4
   

= 1,973,690.276

The  least accurate number is 7800 with 2 significant figures.

The answer must have 2 significant figures.

Rounded Off Answer is

2,000,000

       Put the number of significant figures above/below each number.

Also multiply by ALL THE NUMBERS in the top and divide by ALL THE NUMBERS in the bottom to get the unrounded off value.

Identify the least accurate number.  It will have the fewest significant figures.

The answer must have the same number of significant figures as the least Accurate Number.

           
B. 0.0329 x 9830.0
----------------------- = ?
910.0 x 2278		      3            5
0.0329 x 9830.0
----------------------- = ?
910.0 x 2278
   4          3
   

= 0.000,156,010,67

The  least accurate number is 0.0329 with 3 significant figures.

The answer must have 3 significant figures.

Rounded Off Answer is 

0.000,156

       Put the number of significant figures above/below each number.

Also multiply by ALL THE NUMBERS in the top and divide by ALL THE NUMBERS in the bottom to get the unrounded off value.

Identify the least accurate number.  It will have the fewest significant figures.

The answer must have the same number of significant figures as the least Accurate Number.

           
C. 3420 x 60.00
-------------------- = ?
0.5411 x 8888		         3         4
3420 x 60.00
-------------------- = ?
0.5411 x 8888
     4           4
   

= 42.667,360,43

The  least accurate number is 3420 with 3 significant figures.

The answer must have 3 significant figures.

Rounded Off Answer is 

42.7

       Put the number of significant figures above/below each number.

Also multiply by ALL THE NUMBERS in the top and divide by ALL THE NUMBERS in the bottom to get the unrounded off value.

Identify the least accurate number.  It will have the fewest significant figures.

The answer must have the same number of significant figures as the least Accurate Number.

            
D. 98600 x 0.00004
----------------------- = ?
4297 x 3.654		      3             1
98600 x 0.00004
----------------------- = ?
4297 x 3.654
   4          4
   

= 0.000,251,190,38

The  least accurate number is 0.00004 with 1 significant figure.

The answer must have 1 significant figure.

Rounded Off Answer is 

0.0003

       Put the number of significant figures above/below each number.

Also multiply by ALL THE NUMBERS in the top and divide by ALL THE NUMBERS in the bottom to get the unrounded off value.

Identify the least accurate number.  It will have the fewest significant figures.

The answer must have the same number of significant figures as the least Accurate Number.

   
   
   		    

   
2. A.       4870
    23134
  +      43.9
--------------

            

       4870
    23134
  +      43.9
--------------
    

= 28,047.9

The  least accurate number is 4870 because its last significant figure is 2 places to the left of the decimal point.

The Answer must have its last significant figure 2 places to the left of the decimal point.

Rounded Off Answer is

28,050

       First identify the last significant figure in each number.  I will identify by showing it in green.  

Also calculate the unrounded off answer.

Identify the least accurate number by starting from the left.  It will be the first last significant figure you get to when you start from the left and move right.

The answer must be rounded off to the same position as the least accurate number.

           
B.     0.006778
    0.0321
 + 0.00093
----------------

   

     0.006778
    0.0321
 + 0.00093
----------------
   

= 0.039,808

The  least accurate number is 0.0321 because its last significant figure is 4 places to the right of the decimal point.

The Answer must have its last significant figure 4 places to the right of the decimal point.

Rounded Off Answer is

0.0398

       First identify the last significant figure in each number.  I will identify by showing it in green.  

Also calculate the unrounded off answer.

Identify the least accurate number by starting from the left.  It will be the first last significant figure you get to when you start from the left and move right.

The answer must be rounded off to the same position as the least accurate number.

           
C.       0.00340
      0.00212
  +  6.115
----------------

   

       0.00340
      0.00212
  +  6.115
----------------
    

= 6.120,52

The  least accurate number is 6.115 because its last significant figure is 3 places to the right of the decimal point.

The Answer must have its last significant figure 3 places to the right of the decimal point.

Rounded Off Answer is

6.121

       First identify the last significant figure in each number.  I will identify by showing it in green.  

Also calculate the unrounded off answer.

Identify the least accurate number by starting from the left.  It will be the first last significant figure you get to when you start from the left and move right.

The answer must be rounded off to the same position as the least accurate number.

             
D.       5411
          96.8
+   7250
---------------		       5411
          96.8
+   7250
---------------
   

= 12,757.8

The  least accurate number is 7250 because its last significant figure is 2 places to the left of the decimal point.

The Answer must have its last significant figure 2 places to the left of the decimal point.

Rounded Off Answer is

12,760

       First identify the last significant figure in each number.  I will identify by showing it in green.  

Also calculate the unrounded off answer.

Identify the least accurate number by starting from the left.  It will be the first last significant figure you get to when you start from the left and move right.

The answer must be rounded off to the same position as the least accurate number.

   
  
  		    

   

    

   
3. A. log(64800) = ? log(64800) = ?

There are 3  significant figures in 6480.

Unrounded off logarithm is 4.811,575,006

The answer must have 3  significant figures to the right of the decimal point.

Rounded Off Answer is

4.812

       Determine the number of  significant figures in the number.

In logarithms the only  significant figures are to the right of the decimal point.

The logarithm must have the same number of  significant figures as the original number.
           
B. log(4.211 x 10 -5) log(4.211 x 10 -5)

There are 4 significant figures in 4.211 x 10 -5.

Unrounded off logarithm is -4.375,614,759

The answer must have 4  significant figures to the right of the decimal point.

Rounded Off Answer is

-4.3756

       Determine the number of  significant figures in the number.

In logarithms the only  significant figures are to the right of the decimal point.

The logarithm must have the same number of  significant figures as the original number.
           
C. antilog(3.211) = ? antilog(3.211) = ?

3.211 has 3 significant figures.

Unrounded off logarithm is 

1625.548756

The antilog must have  3 significant figures.

Rounded Off Answer is

1630

       You only find antilogs of logs.  Determine the number of  significant figures in the logarithm.  In logarithms the only  significant figures are to the right of the decimal point.

The antilog must have the same number of  significant figures as the original logarithm.
             
D. antilog( -6.33) = ? antilog( -6.33) = ?

-6.33 has 2 significant figures.

Unrounded off logarithm is 

4.677351413 x 10 -7 

The antilog must have  2 significant figures.

Rounded Off Answer is

4.7 x 10 -7 

       You only find antilogs of logs.  Determine the number of  significant figures in the logarithm.  In logarithms the only  significant figures are to the right of the decimal point.

The antilog must have the same number of  significant figures as the original logarithm.

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