Dimensional Analysis - Mrs Larson's Classes空间分析-拉尔森夫人的类
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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
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
5.6 x 102 = 560
I f the exponent is negative, your final number should be smaller than 1
5.6 xห้องสมุดไป่ตู้10-2 = 0.056
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
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:
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
Dimensional Analysis
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
You should memorize:
Kilo 1 x 103 base units or 1000 base units
So 1 km = 1000 m
Centi 1 x 10-2 base units or 0.01 base units
So 1 cm = 0.01 m OR 100 cm = 1 m
Milli 1 x 10-3 base units or 0.001 base units
So 1 mm = 0.001 m OR 1000 mm = 1m
Be able to use a chart for the others!
On the chart, use 1 with the prefix. Use the other number with the base unit (L, m, g)
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
and division.
Focus on cancelation of UNITS Just another method of unit conversion
First- learn the metric prefixes
essex1/people/speer/large.html
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
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
5.6 x 102 = 560
I f the exponent is negative, your final number should be smaller than 1
5.6 xห้องสมุดไป่ตู้10-2 = 0.056
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
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:
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
Dimensional Analysis
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
You should memorize:
Kilo 1 x 103 base units or 1000 base units
So 1 km = 1000 m
Centi 1 x 10-2 base units or 0.01 base units
So 1 cm = 0.01 m OR 100 cm = 1 m
Milli 1 x 10-3 base units or 0.001 base units
So 1 mm = 0.001 m OR 1000 mm = 1m
Be able to use a chart for the others!
On the chart, use 1 with the prefix. Use the other number with the base unit (L, m, g)
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
and division.
Focus on cancelation of UNITS Just another method of unit conversion
First- learn the metric prefixes
essex1/people/speer/large.html