Journal 9/22/15 Why do we need to convert units? For reference, how big is a cubit? How much money is a talent? How much does a stone weigh? What unit conversions do you know? Objective Tonight’s Homework To learn how to convert units easily Finish the dimensional analysis practice

Dimensional Analysis We’ve encountered a few problems where our units don’t match. Example: We’re given m/s, but the answer needs to be in km/hr. So how do we change units? (We call this process “Dimensional Analysis”. There’s an easy way and a hard way. You’re going to learn the easy way.

Dimensional Analysis Example: Convert 351 m/s to km/s.

Dimensional Analysis Example: Convert 351 m/s to km/s. First, we set up our number to change as a fraction. 351 m s Next, we compare what units we have to what units we want.

Dimensional Analysis We want to change meters to kilometers. To change units, we need to introduce “km” and cancel out “m”. How do we cancel? Same as with numbers. If we have the same unit on top and bottom of a fraction, it will cancel. So in this case, to change, we want to put “km” on the top and “m” on the bottom. 351 m _____km s m We’ve left a blank space to put in the numerical relationship between the two.

Dimensional Analysis Next, we want to add the new numbers. What’s the relationship between meters and kilometers? 1000 m is the same thing as 1 km. To know which number goes on top and which goes on bottom, look at the sentence we just said. “1000 m is the same thing as 1 km.” Pair them up the way you say the relationship. 351 m _1 km s 1000 m Now we’re ready to cross out units and deal with the numbers.

Dimensional Analysis We cross out units that are on top and bottom and write what’s left for the final answer. (Make sure your units still properly represent the kind of answer you’re looking for! Ex: velocity in distance/time) 351 m _1 km_____km s 1000 m s Last, we can deal with the numbers. 351_0.351 km/s 1000

Dimensional Analysis This was a particularly easy example of dimensional analysis, but they will definitely get harder as we go. You can also convert units in steps. Example: seconds  minutes  hours Or you can convert all in one go. Example: seconds  hours As long as you know the numerical relationship between the 2 units, you can convert.

Dimensional Analysis Practice A high school athlete runs 1.00 x 10 2 m in s. What is the velocity in m/s and km/h? A person walks 13 km in 2.0 h. What is the person’s average velocity in km/h and m/s? A glacier can move approximately 12 inches in a year. What is it’s speed in miles / hour? Manually convert 1 mile into kilometers. Do this by converting down to inches, over to centimeters and up to kilometers. Find the number of seconds in a year. Some bullets travel around 1000 m/s. Convert this to miles / hr.

Exit Question $150 dollars a day is the same as what annual salary? (hint: how much do people work in a day, or a year?) a) $33,500 b) $35,000 c) $36,500 d) $38,000 e) $39,000 f) $41,000