Dimensional Analysis

What happens when you divide a number by itself?

What happens when you divide a unit by itself?

In both cases, you get the number 1. Dimensional analysis involves

multiplication and division. Focus on cancelation of UNITS Just another method of unit conversion

Conversion factors To convert between units: Figure out what CONVERSION

FACTOR you need to perform your calculation Conversion factors – take a definition and

turn it into a fraction equal to one – for example: There are 12 inches in 1 foot 12 inches or 1 foot

1 foot 12 inches

Examples of dimensional analysis

Multiply across the top. Divide by whatever’s on the bottom

Examples of dimensional analysis Convert 2.6 km to mm

First- what is the desired unit? Answer- mm

Second- how to we get from m to mm? We know that 1 km = 1000 m We know that 1 m = 1000 mm

2.6 km( 1000 m )(1000 mm) = 2600000 m

1 km 1 m

Scientific Notation

Why do we need to know this? It’s hard to work with numbers like this: 6,000,000,000,000,000,000,000 Or this 0.00000000000000000000876

What is scientific notation? Simplifying large or small numbers by

converting them to a number between 1 and 10 multiplied by powers of 10

Scientific Notation

Powers of 10? 10 x 10 x 10 = 1000 or 103

10-n = 1/10n So 10-3 = 1/103 = 1/1000 = 0.001

Converting regular notation to Scientific Notation Always move the decimal so there is

one number LEFT of the decimal If the original number is LARGER than 1

and the decimal is moved to the LEFT, use a positive exponent 1,567 = 1.567 x 103

If the original number is SMALLER than 1 and the decimal is moved to the RIGHT, use a negative exponent 0.0000045 = 4.5 x 10-6

Converting from scientific notation to regular notation Move the decimal the number of

places indicated by the exponent. If the exponent is positive, your final

number should be larger than 1 5.6 x 102 = 560

I f the exponent is negative, your final number should be smaller than 1 5.6 x 10-2 = 0.056