Uncertainty in Measurements:

Using Significant Figures & Scientific Notation

Unit 1 Scientific Processes

Steinbrink

To understand how uncertainty in a

measurement arises.

Goal:

• Every measurement has some degree of uncertainty

• The uncertainty of a measurement depends on the measuring device.

Types of Digits

• Uncertain digit =

the estimated digit in the measurement---the last digit

• Certain digits = the measurements that are the same with each reading

So what is a Significant Figure?

• The numbers recorded in a measurement (all the certain

numbers plus the first uncertain digit) are the

significant figures

Example

• If a measuring device measures out to the tenths of cm then the uncertain digit would be the hundredths.

Rules for Counting Significant Figures

1. Nonzero integers- nonzero integers always count as significant figures.

Example: The number 1483 has four nonzero integers, which means that the number has 4 significant figures

Zeros

Leading Zeros- precede all the nonzero digits. They never count as significant!

0.00034

This number only has 2 sig figs

Captive Zeros- zeros that fall between nonzero digits. They always count as significant!

12.0092

This number has 6 sig figs

• Trailing zeros- zeros at the right end of the number. They are significant only if the number is written with a decimal point.

100

This number has one sig fig

100.

This number has three sig figs

Rules for Sig Figs in Calculations:Division & Multiplication

• The number of significant figures in the answer is the same as that in the measurement with the smallest number of sig figs.

4.56 x 1.4 = 6.384 6.4

8.315/298 = 0.0279027 .0279

*Based on smallest number of sig figs not decimal places

Rules for Using Sig Figs in Calculations

• Addition or Subtraction– The limiting term is the one with the smallest number of

decimal places.

12.1118.0 limiting-- one decimal

place + 1.013 31.123 31.1

**Only count the number of decimal places**

Scientific Notation

• A method of expressing a quantity as a number multiplied by 10 to the appropriate power.

• For Example: – 4.5 x 103 is the same as 4,500

– 6.06 x 10-3 is the same as .00606

– 0.0015 in scientific notation is 1.5 x 10-3

– 800,000. In scientific notation is 8.0 x 105

– Negative superscript # gets smaller

– Positive superscript # gets larger

More on Scientific Notation

• A positive exponent means you move the decimal to the right and the number in standard form will appear larger

• A negative exponent means you move the decimal to the left and the number in standard for will appear smaller