Fractions, decimals and percentages are frequently used in everyday life. Knowing how to convert between them improves general number work and problem-solving skills. To convert a decimal to a fraction, use place value. The first number after the decimal place is worth tenths, the next is worth hundredths, the next thousandths and so on. Once a number is written as a decimal, it can be converted to a percentage. Remember that 'per cent' means 'per hundred', so converting from a decimal to a percentage can be done by multiplying by 100 (move the digits two places to the left).

Okay, we're looking at converting between fractions, decimals and percentages. So we're going to start off with the nicest of the six combinations. That's going to be decimals two percentages. So let's talk about pizza. So if I've got one whole pizza, what, I've got 1.0 pizzas, I've got one pizza.

This is the exact same to having as having 100% of my pizza. I bought 100% of a pizza. And so because these things are the exact same, they're just different ways of talking about the same thing, I know that 1.0 is the exact same as 100%. Well, how do I get from 1.0 to 100? What I do is I times by 100.

And in general, that's what we do. Imagine we've got no .12. I can times this by 100 and that should give me my percentage, right? I just move this whole thing up two spaces or the decimal point will move down two spaces and it'll end up there. So I get 12%.

So that's our decimal percentages, decimals, two fractions. Let's stick with this example. Let's stick with zero.

And if I want to convert this into a fraction, well, I could be super lazy and just write this as 0.12 over one, right? That's technically a fraction, but we don't tend to want to have decimal points in our fractions. So what we can do is we can make sure that we can get rid of this decimal point. How do I do that? In this case, I can times it by 100 or I can times the top and the bottom by 100.

I know that becomes twelve and the one becomes 100. And this is a much better fraction. Now we could simplify further. So I've got a common factor of two in the top and the bottom. I could divide them both by two and I get six over 50.

I can do the same thing again, divide by two, I get three over 25. And that would be my answer, converting between fractions and percentages. Next. So this can be nice or horrible, depending on what the question is. We'll do a nice one here and we'll do a horrible one here.

So these two methods are very similar. Let's start with maybe three eight and we want to convert this into a percentage. Well, even if we don't know what one 8th is, we're going to kind of work up from the bottom and kind of add our way to going three eight. We know what a half is, right? We know half is the exact same as 50%.

We know a quarter is the exact same as 25%. We're just halving both sides. I can have both sides again and again, 8.5%. And so I can think of three eight as just three lots of one eight, right? It's just three lots of one eight.

So I can think of this as three times an 8th. Well, I know what one eight is. I know one 8th is 12.5%. I just worked that out here. So I can think of this as three times twelve and that gives me 37.5%.

And that would be my answer, that we're kind of using our fundamental understanding of what a half is to kind of get to the stage that we can then kind of count up in eighths, converting fractions to decimals. So, yeah, very similar to fractions of percentages because we know decimals and percentages are very similar. They're just 100 times kind of separated. So fractions of decimals. Let's look at a more horrible question.

Let's go for, say, 1960. Well, this is just 19 divided by 60, right? A fraction is just the same as writing 19 divided by 60. And what do we do when we've got this? Well, normally when we do division, we take our number, we put it under the bus stop and we do the bus stop method.

And I'm going to give myself a few extra zeros because obviously 19 is smaller than 60. So we're going to continue on down into our decimal places. So we did 19 divided by 60. Well, first of all, we do the 60 going to one. No, it doesn't go.

We carry the one. The 60 going to 19. Nope, it doesn't go. We carry the 19 and then we do 60 into 190. Well, I know 60 times three gives me 180, right?

So another 360 can fit. In total, I've got a remainder of ten and now I do 60 into 100. Well, I know that 60 fits into 100 just once with a remains of 40. I now do 60 to 400. Well, because I know my six times tables.

I know six times 60 is 360. So, like, if it's 660 into 400 with the remainder of 40, and I just done this right, I know 60 fits into 406 whole times with the remainder of 40. And what we find is we're basically stuck in this neverending loop. We can keep basically doing this and adding on sixes. Well, we've basically solved it, right?

We know that our answer is therefore going to be 0.316 recurring for this one because we just get never running six s. Percentage to decimals. This is quite nice. It's just the opposite of this. From decimals to percentage, we times by 100.

From percentage to decimals, we just divide by 100.

For example, 12%, we just divide this by 100. Obviously, that decimal point next to the two is going to shift up two spaces. We're going to end up with 0.12. And obviously that's the same as what we started with here. So we're just kind of going back the other way.

Finally, percentages to fractions, this is very similar to percentages to decimals.

As an example, let's say we want 56% and we want this as a fraction. Well, per cent just means per 100, right? So I can think of this as 56 per 100 or 5600. And that's what this is, right? Obviously 100%, which is 100 over 100, which is just one or one whole one.

So we've got 56 over 100. We've got our fraction here, right? But we can probably simplify this down. We've got a common factor, I can see, of two in the top and the bottom. So I could write this as 28 over 50.

I could write this again, common factor of two. This is going to be 14 over 25. And I think that's as far as I can go. There's not any more common factors. All right, let's do a couple of exam style questions.

So we'll look at 54% as a decimal. Well, we know how to do this, right? We know that 100% is just equal to one. And so I know that to convert between the two, I want to divide by 100. But in this case, 54.4 divided by 100 is going to give me zero point 54.

And it's as simple as that. If you can read by force, 00:56 as a fraction, well, again, we can be really lazy and just write this as zero point 256 over one, that's ten to be a fraction. But we don't want to have any decimal places or decimal points in our numbers. So how can I get rid of this decimal point? Well, at the moment, if I look at this, I've got a digit in my thousandths column.

And so to get all three digits out of being on the right of the decimal point, I've got a times by 1000, times by 1000 on the top and the bottom. This is going to give me two, five, six over 1000. We can simplify further. Right, we've got a common factor of T. We could write this as one, two, eight over 500.

Again, I got a common factor of T. This is 64 over T, 50. And again, I've got a common factor of T. This is 32, one, two, five. And I don't think I can go any further than that.

So that's going to be my final answer, finally. 17 over 40 as a decimal. Well, just like we did before, if we think of this as basically 17 divided by 14, what all we're doing here is bus stop method, right? We've got the bus stop moving 17.00. We know we're going to probably need some decimal numbers.

Divided by 40 or 40 goes into 10 times, it goes into 170 times. So it carries 17, it goes into 174 times, right? Four times 40 gives me 160. I want 170. So I've got ten leftover.

40 goes into 102 times, right? Because two times 40 is 80. I've got another 20 left. Over 40 into 200 is going to go five times within remainders. So our answer, again, don't forget to point out our answer is going to be 00:45.

And that's the end of converting fractions, decimals and percentages.

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