- Solutions 16

(c) The Vehicle Assembly Building at the Kennedy Space Center in Florida has a volume of 3,666,500 m^{3}. Convert this volume to liters and express the result in standard exponential notation.

So in this question they tell us that the volume of vehicle in the Kannedy centre is 3,666,500 meters cubed. So we want to convert meters cubed into litres, and they want us to express the result in the standard exponential notation. So how do we go from meters cubed to litres, well there's a connection between centimetres cubed and millilitres. So if you convert meters cubed to centimetres cubed. Then we can convert to millilitres and then from millilitres we could go to litres., so lets begin. So we have 3,666,500 meters cubed, so to convert meters to centimetres, meters goes on the bottom and centimetres ges on the top. But wait this is cubed, right so we have to cube the entire parentheses, 1 goes wherever there's a prefix and centi is 10 to the negative 2. Meters gets placed on the bottom because we want to cancel out meters with meters, so we're left with centimetres. Remember when you cube something it is distributed to everything that's in the parenthese, the numbers and the units. So this becomes 1 cubed times centimetres cubed over 10 to the negative 2 cubed times meters cubed, so everything gets cubed.

So now we're at centimetres cubed and we know that 1 centimetres cubed equals 1 millimetres. So centimetres gets cancelled out and to convert from millilitres to litres we are going from our prefix to a base unit. So we're going from millilitres to litres, millilitres gets placed on the bottom because you want to cancel it out and you're left with litres, which is the unit that we're looking for, 1 goes wherever there's a prefix and milli is 10 to the negative. So multiply everything on the top and divide by everything on the bottom and your final answer should be 3.67 times 10 to the 9 litres. So once again its important to notice the units and the exponents and this is how we express the answer in exponential notation. See you guys soon.