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Convert 400 kilometres per hour to metres per second, giving your answer correct to one decimal place.
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The first thing we wanna do is take 400 kilometres per hour and write it as a fraction, where the numerator is 400 kilometres and the denominator is one hour.
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In our units we have kilometres in the numerator and hours in the denominator.
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We need to convert the kilometres to metres and the hours to seconds, so that, in the end, we have some number of metres per one second.
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To do this, we’ll convert the kilometres to metres first and then convert the hours to seconds.
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We should remember that one kilometre is 1000 metres.
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But we need to be really careful about what goes in the numerator and what goes in the denominator.
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Right now, we have kilometres in the numerator.
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And we want to get rid of the kilometres.
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And that means we’ll have to put the kilometres in the denominator.
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One kilometre is equal to 1000 metres.
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Since 1000 metres is equal to one kilometre, we’re multiplying this value by one.
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We’re not changing its value.
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We’re only changing the units.
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What we’ve done is we’ve taken the kilometres in the numerator and the kilometres in the denominator and cancel them out.
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And so we can say that 400 kilometres per hour will be equal to 400 times 1000 metres per hour.
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We’ve completed the first step as we now have our units in metres.
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We could multiply everything now.
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But since we have more conversions to do, we’ll save that for the final step.
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Now, we need to look at our time units, hours.
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Not everyone memorizes how many seconds are in one hour.
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But we do know how many minutes are in one hour.
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One hour equals 60 minutes and one minute equals 60 seconds.
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We’ll need to use both of these values to make our conversion.
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This time we have hours in the denominator and we want to get rid of that.
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So we need to put our hours in the numerator.
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We can convert from hours to minutes.
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One hour is 60 minutes.
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We’ve now taken our hours in the denominator and our hours in the numerator and cancel them out.
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We currently have metres per minute.
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Again, we’re multiplying by a value of one.
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One hour is 60 minutes.
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And so in our final step, we’ll convert the minutes to seconds.
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One minute equals 60 seconds.
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We have minutes in the denominator, and in the numerator they cancel out.
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And the units we’re left with are metres per second.
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The numerator is 400 times 1000 times one times one metres.
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And the denominator is one times one times 60 times 60 seconds.
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If we rewrite the numerator to say four times 100000 metres and the denominator I have six times six, which equals 36, and 10 times 10, which equals 100, it makes the simplifying a little bit easier.
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Four goes into 36 nine times.
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So we can rewrite four over 36 as one over nine.
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And we can get rid of the 100 and two zeroes in our numerator.
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100000 divided by 100 equals 1000, which leaves us with 1000 metres for every nine seconds.
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We need how many metres it would be for one second.
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To get a one in the denominator, we divide by nine.
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And if we divide by nine in the denominator, we need to divide by nine In the numerator.
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1000 divided by nine equals 111.1 repeating.
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This would be equal to 111.11111 continuing.
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To round to one decimal place, we’ll look to the right, to the hundredth place, where there’s also a one.
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And so we would round down.
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The one in the tenth place stays the same.
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And everything to the left stays the same as well.
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400 kilometres per hour is the same thing as 111.1 metres per second.