Convert to decimals
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please explain this part 1/250 = 100/25*1/1000
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@brilliantyak we can first look at 100/25 wich is 4. Then, there is 4*1/1000, so it is also 4/1000. Last, we divide both the numerater and denominater by 4, which makes 1/250.
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@eeveelution You are correct, however the actual solution actually unsimplifies it. It goes from \(\frac{1}{250}\) and unsimplifies it to \(\frac{100}{25} \cdot \frac{1}{1000}\). That's weird, right? Why would you make it more complicated?
Well, @brilliantyak, to answer your question, the whole problem is about converting to decimals. Converting fractions to decimals is easiest when the denominator is some power of \(10\)! So, figuring out what \(\frac{1}{250}\) is as a decimal might be a little difficult. If you can see that it's actually the same as \(\frac{4}{1000}\), way to go! \(\frac{1}{250}=\frac{4}{1000}=0.004\) is the most straightforward way to convert it to a decimal.
But, if you can't see that right away, another way to do it is what they use in the solution. Let's multiply both the numerator and denominator by 10. \(\frac{1}{250} = \frac{10}{2500} \), but that doesn't really help us. So, let's do it again! \(\frac{1}{250}=\frac{100}{25000}\), and here, notice how \(25\) divides evenly into \(100\)! Pulling out a factor of \(1000\) in the denominator gives us that \(\frac{100}{25000}=\frac{1}{1000}\cdot\frac{100}{25}\). This is another simple way to convert it to a decimal. Hope this makes sense
