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Dimensional Analysis

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**Dimensional Analysis Example: 1 in. = 2.54 cm**

Conversion Factors : Fractions in which the numerator and denominator are EQUAL quantities, expressed in different units Example: in. = 2.54 cm Factors: 1 in and cm 2.54 cm in.

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**Conversion Factors 1. Dollars and cents 2. Liters and mL**

Write conversion factors that relate each of the following pairs of units: 1. Dollars and cents 2. Liters and mL 3. Hours and minutes 4. Meters and kilometers

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**How many minutes are in 2.5 hours?**

Sample Problem How many minutes are in 2.5 hours? Conversion factors: 1hr or 60min 60min hr cancel 2.5 hr x 60min 1hr = min By using dimensional analysis, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!

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**Steps to Problem Solving**

Write down the given amount. Don’t forget the units! Multiply by a conversion faction. Use the fraction as a conversion factor The denomninator is the given The numerator is what you are looking If you can’t convert directly, use one that you know and keep converting Multiply and divide the units (Cancel) Multiply and divide the numbers. Write the answer

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Let’s try it! What units do we use to measure time? (list from smallest to biggest) How many seconds in a year?

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Check Point Use the steps to solving a problem to answer the next questions: How rattlesnake is 2.44 m long. How long is the snake in cm? How many seconds are in 1.4 years? You have $7.25 in your pocket in quarters. How many quarters do you have? If Jacob stands on Spencer’s shoulders, they are two and a half yards high. How many inches is that? (1 yard = 3 ft., 12in = 1ft.)

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Worksheet

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**Check Point #2 Solve using dimensional analysis:**

You have $7.25 in your pocket in quarters. How many quarters do you have? If Jacob stands on Spencer’s shoulders, they are two and a half yards high. How many inches is that? (1 yard = 3 ft., 12in = 1ft.)

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**Jaberwacky problem There are 20 tumtum trees in the tulgey wood.**

In each tulgey wood is one frumious Bandersnatch. There are 5 slithy toves in 2 borogoves. There are 2 mome raths per Jabberwock. There are 2 Jubjub birds in 200 tumtum trees. There are 200 mome raths in each borogove. There are 5 Jubjub birds per slithy tove. The question is: If there are 5 frumious Bandersnatches, how many Jabberwocks are there? You should use a dimensional analysis setup to show your work! HINT: What information above is a conversion factor and what information is not?

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REALLY, REALLY SMALL NUMBERS.

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