Significant Figures and Scientific Notation

Ms. Cannon

Accuracy versus Precision

• Accuracy – A measurement of how close a measurement comes to the _________ or _______ value

• Precision – A measure of how close a ________ of measurements are to one another; repeatable

• Accurate. The average is accurate, but NOT _________.

• Precise, but NOT __________.

• Accurate AND Precise!!

Rules for Working With Significant Figures1. All numbers from 1 to 9 are ALWAYS significant!

Example: 3 ___ Sig Fig

2. Leading zeros are NEVER significant. Examples: 0.00061 ___ Sig Figs or

0284 ___ Sig Figs3. Imbedded zeros are ALWAYS significant.

Example: 60002 ___ Sig Figs or 1403 ___ Sig Figs

4. Trailing zeros are significant ONLY if the decimal point is specified.

Example: 830 ___ Sig Figs 750. ___ Sig Figs

830.0 ___ Sig Figs

Example Number of Significant Figures

• 0.00682 ___

• Rule #2: Leading zeros are not significant. • Example Number of Significant Figures • 1.072

___ • Rule #3: Imbedded zeros are always

significant.

• Example Number of Significant Figures • 300

• Rule #4: Trailing zeros are significant only if the decimal point is specified.

• Example Number of Significant Figures • 300.

• 300.0

• Multiplication or Division:Round the answer to _______ number of significant figures as number with the _______ number of significant figures.

Rules for Working With Significant Figures

Rules for Working With Significant Figures

• Addition or Subtraction:Round result to _______ number of decimal spaces as number with ______ decimal spaces.

General Rule for Rounding• General rule for rounding:• If the number you are rounding is followed by

5, 6, 7, 8, or 9, round the number ______.– Example: 38 rounded to the nearest ten is 40

• If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number _______.– Example: 33 rounded to the nearest ten is 30

Exact and Inexact Numbers• There are two kinds of numbers in the world: • Exact • Inexact

• Exact: –example: There are exactly 12 eggs in a

dozen. –example: Most people have exactly 10

fingers and 10 toes.

Exact and Inexact Numbers• Inexact numbers: – Example: any measurement.– If I quickly measure the width of a piece of

notebook paper, I might get 220 mm (2 significant figures). – If I am more precise, I might get 216 mm (3

significant figures). –An even more precise measurement would

be 215.6 mm (4 significant figures).

Scientific Notation

• In any effort to reduce the cumbersome nature of very large and very small numbers, scientists and engineers use ____________ ____________.

• This removes the problem of excessive leading and trailing ___________.

Scientific Notation

• Standard Form• _________._________ X 10Exp.

Ones Place.10th Place

• Example: 2.6 x 104

How do you change a number into Scientific Notation?

• Example 1) 1047Step 1: Find the decimal? • At the end of the number _______Step 2: Move the decimal to the left • _______ (decimal moved ____ decimal places)Step 3: The exponent equals the number of decimal

places and is positive because moved decimal to the left

• ______________ Rounds to _____________

How do you change a number into Scientific Notation?

• Example 2) 0.00005432Step 1: Find the decimal?• At the beginning of the number 0.00005432Step 2: Move the decimal to the right• _________(decimal place moved ___ places)Step 3: The exponent equals the number of decimal

places and is negative because moved decimal to the right

• ______________ Rounds to ___________

Practice Problems

• Complete the following chart: