Algebra

Converting fractions to decimals | Decimals | Pre-Algebra | Khan Academy

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Now I will show you how the fracture turned To decimal And if we have time, perhaps we will learn how to do Converts a decimal number to a fraction So let’s get started With an example Let’s start with the fraction 1/2 And I want to convert it to a decimal And the way I will always succeed with you So all you have to do is take The numerator and divide it by the denominator Let’s see this So we take the denominator of 2, and Divide the numerator by 1 And we’ll say, how can we divide 1 by 2? Well, according to the decimal division rule, we are We can add a decimal point here, so we put 0 Actually, I didn’t change the value of the number itself, however Just to get some precision here We put the decimal point here Is 1 divisible by 2? of course no Rather, 10 is divided by 2, so we divide 10 by 2, and the result is 5 5×2 = 10 The remaining 0 So we did this Thus 1/2 = 0.5 So let’s solve one a little bit more difficult Say 1/3 Well, again, we take the denominator 3 And we divide the numerator by it And I’m going to add some zeros here Well, 1 does not divide by 3 And 3/10 = 3 3×3 = 9 Let’s subtract 0 and let the rest 1 3/10 = 3 And we put the decimal point here 3×3 = 9 Do you see something special here? We get the same output As you can see 0.3333 continuously In fact, there is no way to write An infinite number of 3 All you can do is write 0.33 As a short style for the frequent number 0.33 Or you can write it as 0.3 Although I tend to see this often maybe Im wrong But in general, this line is above the decimal point It means that the number is repeated infinity So 1/3 = 0.33333 repeated Here is another way to write 0.33 repetition Let’s continue with a little more difficult examples, but they are They all follow the same pattern Let me choose some strange numbers I would choose a break as follows Let it be 9/17 this is interesting The numerator here is greater than the denominator In this case we will get a number greater than 1 But let’s solve the issue So we take 17 and divide it by 9 And we add zeros to the decimal point here Now 9/17 = 1 1/9 = 9 9-17 = 8 We go down 0 80/9, well, we know 9×9 = 81, then So in this case we can divide by 8, because the number is not acceptable Divide by 9 P 8×9 = 72 80-72 = 8 We go down another 0 Here we see another pattern 80/9 = 8 8×9 = 72 It is clear that I can continue to do so forever And we’ll keep getting 8 Thus, the result of 9/17 = 1.88 while 0.88 An infinite number Or, if we want to rotate that, let’s say It = 1 approximately, depending on what We recycle it, of course We could say roughly 1.89 We can spin it somewhere else I rotated it in the hundreds position But that is the answer 9/17 = 1.88 Actually the number can be written separately, but how can we write it? As one connected number? Well, I will write it separately I don’t want to mix things up with you now Let us now solve more problems Let me just sort of solve a rather strange matter Let it be 17/93 How much is it in decimal numbers? Also, we do the same 93 be divided, and I will draw a long line here because I am I don’t know how many decimal places the result will contain And remember, the denominator is the divisor The numerator is the divisor This type of issue is kind of confusing because we are used to Divide the larger number by the smaller number So 17/93 = 0 This is a decimal point here So how much is the result of 170/93? The output is 1 1×93 = 93 170-93 = 77 We go down 0 What is the output of 770/93? lets see Let me do that, I think it’s equal to 8 8×3 = 24 8×9 = 72 + 2 = 74 And then we lay down 10 and 6 Output 26 We go down another 0 93/26 = 2 2×3 = 6 18 This is 74 0 Even we can continue We can put more decimal places This can be done indefinitely But if you want to get an approximation for that, you can Say that 17/93 = 0.182 f Then the decimal places will continue And you can still do that if you want But if this happens in an exam, you can To stand at a certain point Or it can be rotated to the nearest hundreds or Status of thousands Now, let’s try to convert it another way From a decimal number to a fraction I think you will find this Much easier May I ask how to write 0.035 with fractions? Well, the decimal number 0.035 can be written with fractions As such, it can be written as well 03 Well, I shouldn’t type 035 This is the same thing as 35/1000 And probably you will ask, how I knew that Well because we went to 3, by the way she is in the dozens Remember that the 10’s place is not the number 10 This is the rank of hundreds Here is the status of thousands So this is how we walked about 3 decimal places This is 35 per thousand If the decimal point is let me say, if it is 0.030 There are several ways to say this Well, we could say we’ve reached 3 and are in position Thousands So this number has the same value as 30/1000 or Also, it could be said, 0.030 is the same thing 0.03 because the last zero has no value If we have the number 0.03 then we automatically go to the rank of hundreds It has the same value as 3/100 So let me ask you, are these numbers equal? Well, yes They are If we divide both the numerator and the denominator On 10 we’ll get 3/100 Let us now go to this issue Have we solved it? Is 35/100, I mean, yeah that’s right This is broken 35/1000 But if we want to simplify it in the simplest form Divide the numerator and denominator by 5 And thus we get the simplest picture It is 7/200 If we want to convert the fraction 7/200 to a decimal using The same way, we can divide 200 by 7 And we get 0.035 I will leave this issue to you as a duty that you can do on your own I hope you have learned the basic principles Converts fractions to decimal and vice versa And if you don’t, just do some exercises I will try to record some other exercises for you Or other offers Enjoy doing exercise

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