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Section 3.1, Part 1: Measurements and Their Uncertainty

Measurements and Their Uncertainty

On January 4, 2004, the Mars Exploration Rover Spirit landed on Mars. Each day of its mission, Spirit recorded measurements for analysis. In the chemistry laboratory, you must strive for accuracy and precision in your measurements.

Using and Expressing Measurements

A is a quantity that has both a number and a unit.

Measurements are fundamental to the sciences. For that reason, it is important to be able to make measurements and to decide whether a measurement is .

Using and Expressing Measurements

In notation, a given number is written as the product of two numbers: a coefficient and 10 raised to a power.

The number of stars in a galaxy is an example of an estimate that should be expressed in scientific notation.

NOTE: The coefficient must be between and

Scientific Notation

To turn a number into scientific notation:

  1. Determine where the point is and where it should go.
  2. Count the number of places you need to move it: THIS IS YOUR .
  3. Write the followed by "x 10" raised to the exponent you determined.
  4. Determine if the exponent is positive or negative:
  • Numbers > 1 =
  • Numbers < 1 =

Scientific Notation

Scientific Notation Practice

Turn each number from regular notation to scientific notation:

100,000 = 0.001 =

200 = 0.000 02 =

45,000 = 0.03 =

3,200 = 0.000 53 =

8,900,000= 0.000 000 062=

Scientific Notation

To turn a number into regular notation:

  1. Look at the exponent: IT TELLS YOU HOW MANY TO MOVE THE DECIMAL.
  2. Determine which way to move the decimal:
  3. Positive - Make the number
  4. Negative - Make the number
  5. Put in as place holders.

Scientific Notation

Scientific Notation Practice

Turn each number from scientific notation to regular notation:

1.0 x 10-1 = 1.0 x 101 =

1.0 x 10-2 = 2.3 x 103 =

2.0 x 10-3 = 4.2 x 105 =

5.0 x 10-7 = 6.8 x 104 =

3.4 x 10-9 = 9.9 x 1010=

Accuracy and Precision

  • is a measure of how close a measurement comes to the actual or value of whatever is measured.
  • is a measure of how close a of measurements are to one another.

Accuracy, Precision, and Error

To evaluate the of a measurement, the measured value must be compared to the value.

To evaluate the of a measurement, you must compare the values of two or more measurements.

Accuracy, Precision, and Error

Determining Error

  • The value is the correct value based on reliable references.
  • The value is the value measured in the lab.
  • The difference between the experimental value and the accepted value is called the .
  • Equation:

Accuracy, Precision, and Error

The error is the absolute value of the error divided by the accepted value, multiplied by 100%.

Equation:

Accuracy, Precision, and Error

If I'm boiling water and find that its boiling at 98°C on my thermometer, what is the percent error in my measurement?

Accuracy, Precision, and Error

Just because a measuring device works, you cannot assume it is .The scale below has not been properly zeroed, so the reading obtained for the person’s weight is .

Significant Figures in Measurements

Suppose you estimate a weight that is between 2.4 lb and 2.5 lb to be 2.46 lb. The first two digits (2 and 4) are known. The last digit (6) is an estimate and involves some uncertainty. All three digits convey useful information, however, and are called significant figures.

The figures in a measurement include all of the digits that are known, plus a last digit that is .

Significant Figures in Measurements

must always be reported to the correct number of significant figures because answers often depend on the number of significant figures in the used in the calculation.