dimensional analysis guide

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What’s the best way to solve a Science problem? You should G.U.E.S.S.!! G ivens List each numerical value found in the problem. Include the variable and unit/label for each number. Example: l = 7.1 m w = 9.4 m h = 380 cm = 3.80 m (Note: it is wise to anticipate converting any units during this step) U nknowns Identify what it is that you are trying to find or solve for. Example: v- volume of a large room E quation Write down the equation or set up a blank T-chart that will start you in the right direction. Use only the general form of the equation; DO NOT fill in numbers! v = l x w x h S ubstitution Rewrite the equation or T-chart, but this time substitute in any known/given quantities and conversion factors. Be sure to include all units! v = (7.1 m) x (9.4 m) x (3.8 m) S olution Show all needed work and report your answer with correct units. v = 253.6 m 3

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Learn and review how to solve problems using dimensional analysis (factor-label).

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Page 1: Dimensional Analysis Guide

What’s the best way to solve a Science problem?

You should G.U.E.S.S.!!

Givens List each numerical value found in the problem. Include the variable and unit/label for each number. Example:

l = 7.1 m w = 9.4 m h = 380 cm = 3.80 m

(Note: it is wise to anticipate converting any units during this step)

Unknowns Identify what it is that you are trying to find or solve for. Example: v- volume of a large room

Equation Write down the equation or set up a blank T-chart that will start you in the right direction. Use only the general form of the equation; DO NOT fill in numbers!

v = l x w x h

Substitution Rewrite the equation or T-chart, but this time substitute in any known/given quantities and conversion factors. Be sure to include all units! v = (7.1 m) x (9.4 m) x (3.8 m)

Solution Show all needed work and report your answer with correct units. v = 253.6 m3

Page 2: Dimensional Analysis Guide

Understanding Dimensional Analysis

Dimensional Analysis is just a fancy way of converting things. You convert pennies into dollars by dividing the number of pennies you have by 100. You may not believe it yet, but dimensional analysis is that simple. Example: If you want to convert pennies to dollars you need a conversion factor. We know that 100 pennies = $1, so we set the conversions up like this:

1 dollar Or 100 pennies 100 pennies 1 dollar

Why the two formats? Because as we’ll see in a minute units can only be cancelled when they are on opposite sides (and diagonal) of the dividing line of our T-chart. Example problem #1 Convert 560 pennies to dollars.

1. Identify what we have and what we need:

Given: 560 pennies

Unknown: Number of dollars

2. Set up your conversion factors

100 pennies = 1 dollar

3. Set up your T-chart

560 pennies 1 dollar = (560 x 1) 100 pennies 100

Our answer is $5.60 Example problem #2: Convert 3.25 dollars into pennies.

4. Identify what we have and what we need:

Given: 3.25 dollars

Unknown: Number of pennies

5. Set up your conversion factors

1 dollar = 100 pennies

6. Set up your T-chart

3.25 dollars 100 pennies = (3.25 x 100) 1 dollar 1

Our answer is 325 pennies If you start with the GUESS method and approach all problems the same way you will find they are easier than they seem!