# Converting within the metric system | Pre-Algebra | Khan Academy

. Convert 51.8 decimeters to kilometers Let’s think about what a decimeter means by meaning The meter, then we can think about what the kilometer means in terms of Meter, and then we convert it So we’re going to start with 51.8 decimeters Now, as a starting point, so we keep things simple We will convert them to meters, because this is the prefix Show us a little about how many meters is equal If we want to convert it to meters, the units are It should be meters / decimeter Meter / decimeter And we need it because this is a decimeter and that is a decimeter They will be deleted, and all that’s left are ours It is a meter Now 1 meter is equal to how many decimeter? Well, the creamy prefix means 1/10 So 1 decimeter = 1/10 of a meter In other words, we can say that there are 10 Decimeters in every meter This is a smaller unit 10 of these consist of 1 of these, 1/10 of a meter per Decimeter, which is exactly what we gave 1/10 of a meter Now if you hit those two things, what do you get? Well, the decimeter is omitted, and we divide 51.8 by 10 Multiplying by 1/10 is equivalent to dividing by 10 So this is equal to 51.8 ÷ 10 The decimal point is moved to the left Equals 5.18 So this equals 5.18 meters You should always check Is this logical? Is it logical that 51 decimeters Equal to 5 meters? Well, definitely It should be less We are moving from a small unit to a higher unit, so We must underestimate the higher unit until we have the same The distance in this case The meter is a unit for measuring length Now, we’ve got 5.18 meters, and we want to convert it now to kilometer We want to convert it to kilometers We want to get a meter in the denominator and Miles in the numerator Why? Because this meter and that meter will be deleted Now, how many kilometers is it? The kilo gives us 1,000 This is equal to 1,000 meters So 1,000 meters = 1 kilometer If we want to multiply this, the meter will be deleted We have a kilometer left And multiplying something by 1,000 is equivalent Divide by 1,000, which makes sense You should get a smaller number here because we are moving from Small unit to bigger unit So we would need a much smaller amount Of great unity So this equals 5.18 / 1,000 kilometers Now, the simplest way to do this, if we take 5.18 / 10 = – we’re moving the decimal point down to the left – Equals 0.518 If we take 5.18 and divide it by 100, we will move The decimal point has two places to the left One, two, and we should add 0 here This is equal to 0.0518 And if we take 5.18 and divide it by 1,000, it will We move the decimal point three houses to the left We will do this If you start with 5.18 – the decimal point location here – We’re going to make one, two, so this is 1 0, and then 3 Here is where the decimal point will be Thus or in another way, it is just above 5 / 1,000 This equals 5 / 1,000 It’s just a little higher So the final answer is 51.8 decimeters equal to 0.00518 kilometer Always check Is this logical? Certainly We are moving from a very small unit, a group of Small unit, into a small amount of large unit It makes sense It makes sense that this number will decrease while The unit gets bigger .