Accuracy vs. PrecisionMeasurements need to accurate & precise.

Accurate -(correct) the measurement is close to the true value.

Precise –(reproducible) several measurements are close in value.

Good PrecisionGood Accuracy

Poor PrecisionPoor Accuracy

Good Precision Poor Accuracy

Accuracy vs. Precision

Sources of Error • human (mistakes in experiment, measurements, etc.)

• equipment (faulty or broken equipment, etc.)

Calculating ErrorAccepted Value - true (correct) value - look it up.

Experimental Value - measured in lab

Error = Accepted value - Experimental value

ExampleYou look up the density of water & it is 1 g/ml

You calculate the density in the lab to be 0.8g/ml

Error = 1 g/ml - 0.8g/ml = 0.2 g/ml

Percent ErrorFormula = Accepted value- calculated value x 100

Accepted value ExampleAccepted value for the density of water is 1 g/mlYou calculate the density in the lab to be 0.8g/ml

% error = 0.2 g/ml x 100 = 20% error1 g/ml

• absolute value of the error makes it a positive number • The units cancel out so it is a %

Scientific Notation • the product of two numbers: a coefficient & a

power of 10.

• Ex: 3.6 x 104 .

• the coefficient must be greater than 1 but less than 10.

• there is only one number to the left of decimal. Ex: 1.0- 9.9.

Practice: Write the following in scientific notation:

0.0003=_____________ 3000.0=______________

1343= _____________

0.791= ____________

Scientific Notation on a CalculatorGET OUT YOUR CALCULATOR!!!

• Type in the coefficient (use +/- if needed)• EE or EXP (use 2nd or inv. if needed)• exponent (use +/- if needed)

Example: 3.0 x 104

• Type in 3.0• push the EE or EXP • Type in 4

Multiplying Scientific Notation (practice on your calculator)

 (3.6 x 104) x (2.22 x 10-2) What’s happening? Multiply coefficients and ADD

exponents.

• How to do it on a calculator: • Type in 3.6• push the EE or EXP button• Type in 4 (use +/- if needed)• push multiply• Type in 2.22• push the EE or EXP button• Type in 2 (use +/- if needed)• push =

Dividing Scientific Notation

How to do it on a calculator: Follow the same steps as above but divide instead of multiply

 

(1.98 x 104) =

(2.34 x 10-1) 

What’s happening mathmatically? Divide coefficients & SUBTRACT exponents.

Adding/Subtracting:

5.40 x 103 + 6.0 x 102 =

How to do it on a calculator: Follow the same steps as above but add/subtract instead of multiply.

What’s happening? the exponents are made then same then add/subtract coefficients.