Error and % error

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Error- measured value- Actual Value

Example: Error:

503.5 ft- 500ft= 3.5ft +3.5 ft

502.8 ft- 500ft = 2.8 ft + 2.8

497.4 ft - 500 ft= -2.6 - 2.6

Percent error- /error/ x 100%

Actual value

Example:

3.5/500ft x 100% = 0.7%

2.6/500ft x 100% = 52%

3.5/500ft x 100% = 21%

Percent error= /measured value - actual value/ x 100%

actual value

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EXCERCISE EXAMPLES:

1. A student estimated a mass to be 250g, but upon carefully measuring it, found the actual mass to be 240g. What is the percent error?

250g - 240g= 10 x 100%= 1,000/ 240g= 4.16%

Measured value: 250g

Actual value: 240g

Percent error: 4.16%

2. A student measured the temperature of boiling water and got an experimental reading of 97.5 o C. What is the percent error?

97.5-100= -2.5 x 100%= -250/100%= -2.5%

Measured value: 97.5oC

Actual Value: 100oC

Percent error: 2.5%

3. An experimental measurement was taken of 10.4 mL and the actual measurement was 9.7 mL. What is the percent error?

10.4- 9.7= 0.7x 100%= 70./9.7= 7.21%

Measured Value: 10.4

Actual Value: 9.7

Percent error: 7.21%

4. Experimental = 62.5 g and accepted value = 65.2 g. Solve for percent error.

62.5-65.2= -2.7x100%= -270/65.2= 4.14%

Measured value: 62.5g

Actual value: 65.2g

Percent error: 4.14%

5. Joe measured the volume of an object 5 times, and got results of: 34.5 mL, 34.9mL, 34.2 mL, 33.4 mL, and 35.9mL. What is his average experimental result?

34.5+34.9+34.2+33.4+35.9= 172.9/5= 34.58

6. The actual volume of the object was 34.1 mL. What is the percent error of his average result?

34.58-34=0.48 x 100%=48/34.1= 1.40

Measured Value: 34.58

actual value: 34.1

percent error: 1.40%

7. A student estimated a mass to be 325g, but upon carefully measuring it, found the actual mass to be 342g. What is the percent error?

325-342= -17 x100= -1700/342= 4.97%

Measured Value: 325g

Actual Value: 342g

Percent error: 4.97%

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CLASS EXCERCISE

1. The density of water at 4oC is known to be 1.00 g/mL. Kayla experimentally found the density of water to be 1.075 g/mL. What is her percent error?

1.00-1.075= 0.075 x 100= -7.5/ 1.075= 4.28%

Measured value: 1.00g/mL

Actual Value: 1.075g/mL

Percent error: 4.28%

2. Joshua uses his thermometer and finds the boiling point of ethyl alcohol to be 75o C. He looks in a reference book and finds that the actual boiling point of ethyl alcohol is 80oC. What is his percent error?

75-80= -5x 100%= -500/80= -6.25%

Measured value: 75oC

Actual Value: 80oC

Percent error: -6.25%

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CLASS ACTIVITY FEBURARY 25TH

1. An object has a mass of 35.0 grams. On Anthony’s balance, it weighs 34.85 grams. What is the percent error of his balance?

34.85-35.0= -0.15 X 100= 15/ 35.0= -0.429%

Measured value: 34.85 grams

actual value: 35.0grams

Percent error: 0.429%

2. The concentration determined for an unknown sample of hydrochloric acid by a student is 0.1355 M. According to the instructor’s information, the true molarity (M) of this solution is 0.1364 M. What is the percent error in this experiment?

0.1355- 0.136= -0.0009 x100= -0.09/0.1364= -0.66%

Measured value: 0.1355 M

Actual Value: 0.1364 M

Percent error: 0.659%

3. The melting point of potassium thiocyanate determined by a student in the laboratory turned out to be 174.5 oC. The accepted value of this melting point is 173.2 oC. What is the percent error in this reading?

174.5- 173.2 = 1.3 x100= 130/173.2= 0.75%

Measured Value: 174.5 oC

Actual Value: 173.2 oC

Percent error: 0.750%

4. An object with an actual mass of exactly 0.54 g is given to 2 students. One student obtains a mass of 0.59 g for the object, while another says the mass is 0.49 g. Which of the students, if either has the greater percent error?

0.59-0.54= 0.05 x 100= 5/ 0.54= 9.25%

Measured Value: 0.59 g

Actual Value: 0.54g

Percent error: 9.25%

0.49-0.54= -0.05 x100= -5/ 0.54= 9.25%

Measured Value: 0.49g

Actual Value: -9.25%

Percent error: 9.25%

Both have the same percent error= 9.25%