All data and results in your lab reports must be reported using scientific notation. Scientific Notation makes it easy to report extremely small and large numbers, and to report numbers using the correct number of significant digits. Here is an example:

SCIENTIFIC NOTATION, SIGNIFICANT FIGURES, ANDREADING ERRORS

300250 350

By convention, any number reported without a decimal place is agreed to have an uncertainty of half a digit smaller than the smallest digit reported. The number 300 really means anything between 250 and 350.

295 305299.5 300.5

In Scientific Notation this would be written as3 X 10 2

Now if the first zero in 300 was significant, the the uncertainty range would be as follows:

In Scientific Notation this would be written as3.0 X 10 2

If the second zero in 300 was significant, the the uncertainty range would be as follows:

In Scientific Notation this would be written as3.00 X 10 2

X 103.002

3.00

This is called the mantissa

102

This is called the base

This is called the exponent, or characteristic

SIGNIFICANT DIGITS: Rules for ADDING and MULTIPLYING

6.843+0.001

6.844

In this number there are four significant digits. The least significant

digit is the ‘3’ which is in the third decimal place

In this number there is one significant digit. The only significant digit is the ‘1’ which is in the third

decimal place

31

Find the decimal place of the least significant digit shared by both numbers. 6.843

8 +1

Once again, there are four significant digits in this number. The least significant digit is the ‘3’ which is in the third decimal place.

The only, and therefore significant digit here is the ‘1’.

Find the decimal place of the least significant digit shared by both numbers.

61

This determines the decimal place of the least significant digit in the answer. In this

example, the one’s place.

SIGNIFICANT DIGITS: Rules for ADDING and MULTIPLYING

5.2x 3.1

16

In this number there are two significant digits.

In this number there are two significant digits.

This determines the number of significant figuresin the answer: In this example, two.

Find the number with the least number of significant digits.In this example both numbers have the same number of

significant digits.5.243

16 x 3.1

In this number there are four significant digits

In this number there are twosignificant digits

Find the number with the least number of significant digits.

5.23.1

3.1

The final answer should also have the samenumber of significant digits (two).

SIGNIFICANT DIGITS: Rules for ADDING and MULTIPLYING

When reporting measured values you must include an estimate of the uncertainty in every measurement. Here is an example...

Here you are to measure the distance between two pointson a piece of paper. The dots represent the position of an

air puck at different times. The dots are formed by anelectric spark which leaves a burn mark on the paper.

Here’s a close up of what they look like...

Using the ruler, you measure the distance between these dots and claim it is 1.7cm. How good is the measurement? Is it1.6 to 1.8? Is it 1.699 to 1.701? You must explicitly state therange of values you think are acceptable for the measurement.

As you look even closer you can begin to realize how how important it is to include a range of values. Here are

some factors to consider when finding an acceptable range:

How well can you estimate the center

of a dot?

Does the thickness of the ruler lines affect how well you line up the ruler with the dot?

How well can you estimate a fraction

of the space betweenruler markings?

There are no hard and fast rules for estimatingreading errors. You must learn to make the best

measurements using the measuring devicesavailable under the conditions existing whereand when you take the measurements. And remember, measurements with too large an

uncertainty are almost as useless as nomeasurement at all, while too small an uncertainty

suggest that the data itself is not credible.

A reasonable estimate for the distance would likely be 1.7+/- 3

You have completed the graphing tutorial.

To return to the main lab site click here.

Presentation created by: Craig Fraser