3.1 Measurement and Uncertainty

How do you think scientists ensure measurements are

accurate and precise?

Expressing Measurements Scientific Notation

Coefficient and power of 10

Example – 6.02 x 1023

Useful in expressing very large and very small numbers

What power of 10 would a very small number like 0.00000015 be?

1.5 x 10-7

Is the Measurement Right? Accuracy – How close a measurement is to the actual or

true value.Need actual or true value to compare

Precision – How close a series of measurements are to one

another.Need to have 2 or more repeated measurements

(Dart Board Situation)

Determining Error Accepted Value – Correct value based on reliable reference

Experimental Value – Measurement from the investigation

Error -The difference between the experimental and

accepted values.

Error = Experimental value – Accepted value

Percent Error The absolute value of the error divided by the

accepted value, then multiplied by 100%.

Percent Error = [error]/accepted value x 100%

Why the absolute value of the error?

Practice Measure the mass of your toy car using the

triple beam balance. Use the electronic scale to determine the true

mass value for the toy car. Calculate the percent error for your

measurement. How many significant figures does your mass

measurement have?

Significant Figures All the digits that are know plus the last digit that is

estimated. (Used for the purpose of rounding.) Rules for Sig. Figs.1. All nonzero digits are significant.2. Zeros appearing between nonzero digits are

significant.3. Leftmost zeros appearing in from of nonzero are

not significant (just placeholders). Try sci not.4. Zeros at the end and to the right of a decimal

point are always significant.5. Zeros at the rightmost end that lie to the left of the

decimal point are not significant. Try sci not.6. Exact quantities do not affect the process of

rounding

How many significant figures?1. 0.05730 meters2. 8765 kilograms3. 0.00073 centimeters4. 20 flags5. 40.007 liters6. 8.750 x 10-2 grams

Then round to 2 significant figures.

Significant Figures for Calculations Answer cannot be more precise than the least

precise measurement in which it was calculated from.

Addition and Subtraction2.34 + 45.1 + 8.706 = 56.146Rounded to 56.1 (to the tenth)

Multiplication and Division8.09 x 7.861 x 3.112 = 197.9091649Rounded to 198 (to 3 significant figures)

Do the math and put the answer in the correct number of significant figures.

1. 75.9 m + 8.72 m + 9.8 m 2. 5.66 L – 3.221 L3. 4.90 grams + 17.987 grams4. 3.75 cm – 1.2 cm 5. 12.4 grams + 8.65 grams + 9.214 grams6. 14.2 kilograms – 7.146 kilograms

Do the same with multiplication and division.1. 7.09 meters x 6.2 meters2. 23.5 cm x 8.2 cm x 14.9 cm3. 5467 ml / 14.64. 7875.9 meters x (1 km/1000 meters)5. 3.9823 liters / 43.1 liters6. 678 seconds / 8

Now put your answer in scientific notation.