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- Solutions 34

Express the quantity 254,998 m in each unit.

a. km

b. Mm

c. mm

d. cm

Hey guys, in this question we're asked to convert the following value into its metric prefixes so the number that we're looking at is 254,998 meters so we're going to have to convert meters into different types of metric prefixes so the first one is going to change into kilometers, so we have the number here and we have to convert it to kilometers so meters goes on the bottom kilometers on the top, remember 1 goes with the metric prefix so 1 kilo is 10^3 so this gives me this as my value.

We're going to need room to do the rest guys so let me take myself out of the image so next we have to change it into mega meters so same exact value again you want to get rid of meters so meters on the bottom kilometers on.... Megameters goes on the top so remember here for every 1 mega is 10^6 so we can write this two different ways either 0.254998 mega meters or in scientific notation as 2.54998x10^-1 megameters.

For C, we have to convert it to millimeters so same exact value again and notice the trend all that's really happening is I'm changing the top portion with a new metric prefix and each metric prefix has 10 to some power associated with it so here we have meters on the bottom millimeters on top, 1 milli is 10^-3 so that gives you 2.54998x10^-8 Millimeters.

For a D, we have to change it into centimeters so it's that same exact value again and now we're just going to change it into centimeters, so remember 1 centi is 10^-2 so when we do that we get this as our answer 10^7 centimeters. So, remember all this really required us to do was to transform our base unit in meters to one of these new metric prefixes that can be done in one step as we've seen here so some of them required us to write in the scientific notation being converted in scientific notation or in decimal form.