Units of Measurement

• SI base units

  Page from NIST (National Institute of Standards and Technology) in Washington, D.C.

  Background and historical information about the standard units from NIST.

• Prefixes used in SI units

  Page from NIST in Washington, D.C.

• Derived SI units

  Page from NIST in Washington, D.C.

• Equivalences in measures between SI and English

• Important equivalences in the English measurement system

  12 in = 1 foot 3 feet = 1 yard 5280 ft = 1 mile

  4 quarts = 1 gallon 2 pints = 1 quart

  16 ounces = 1 pound 2000 lbs = 1 ton

Uncertainty in Measurement

Measurements are made in scientific laboratories, and are commonly used in scientific calculations. To carry out scientific calculations properly it is important to discuss the following concepts;

• Accuracy

  • refers to the agreement of a particular value with the true value.

• Precision

  • refers to the degree of agreement among several measurements of the same quantity.

  • Sample animation differentiating between accuracy and precision.

• Exact numbers

  • those numbers that we know exactly. Counting objects is an experiment that can be carried out with complete accuracy.

• Uncertainty

  • . numbers that are not known exactly. When we measure lengths (of an object), volumes (of a liquid) or masses (of a solid) the measurements are not exact, they have some degree of uncertainty.

    Here is a nice WEB site on Uncertainty in Measurement

• Sample animation demonstrating uncertainty in measurement.

• Addition and subtraction

  • When adding or subtracting measured quantities, there should be the same number of decimal places in the answer as there are in the measurement with the least number of decimal places. For addition and subtraction the number of significant figures is NOT important.

• Multiplications and Division

  • When multiplying and dividing measured quantities, there should be as many significant figures in the answer as there are in the measurement with the least number of significant figures.

• Rounding Rules

  Look at the left most digit to be dropped

  • If this digit is '5' or greater, or is '5' followed by nonzero digits, add '1' to the last digit to be retained and drop all the digits further to the right.

  • If this digit is less than '5', drop it and all digits further to the right.

Using Significant Figures (Practice animation )

Here is an additional problem.

• Example Exercise;

Add the following number and report the answer to the correct number of significant figures.

4.56 x 10³ + 8.92 x 10⁴ =

• Solution:

When adding or subtraction number expressed in scientific notation it is critical to write the numbers such that the power ten is raised to is the same for all values. For example both 4.56 x 10³ and 8.921 x 10⁴ must be written to the same power. If we arbitarily select 10³ as the power the two values are;

4.56 x 10³ and 89.2 x 10³

Adding the two numbers gives 93.76 x 10³. Looking at the two values the first value has two places to the right of the decimal point and the second value has only one decimal place. So the answer must be reported to only one place to the right of the decimal when the exponent is 10³. SInce the digit to be dropped is greater than 5 we add 1 to the last digit to be retained and the answer is 93.8 x 10³. Now the number must be written properly in scientific notation, so 93.8 x 10³ becomes 9.38 x 10⁴.

 

Dimensional Analysis/Unit Conversions

Some examples of how dimensional analysis is applied in calculations.

• Sample Exercises

• Example #1

• Example #2