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7.2. OPERATIONS WITH DECIMALS 127 Repeating Decimals (1) Fractions in simplified form with only 2 s and 5 s as prime factors in the denominator convert to terminating decimals. Example. Example.

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In the last section, we learned how to convert some special Base 10 fractions into decimals, and vice versa. Now, were going to learn how to convert ANY fraction into a decimal. And it turns out to be really simple… all you have to do is divide. Since a fraction is really just a division problem, if you go ahead and DO the division, you’ll get an answer, and that answer will be the decimal value of the fraction. Now there are two ways we can do the division …the easy way, and the hard way. Now just because I’m mean, we’re going to start with the hard way. Let’s take the fraction one-half and convert it into a regular division problem with this division symbol. Now, all we have to do is follow the procedure for division. We just see how many times this ‘2’ divides into this ‘1’. Uh Oh! It won’t divide any times. ‘2’ is bigger than ‘1’. …looks like we’re going to need some help, and that’s where the decimal point comes in. Now you remember that in the last section, we learned that ‘1’ could be written as 1.0 or 1.001,000.000 and its value is still ‘1’. Let’s try doing that here and see what happens. After the ‘1’, put a decimal point and then a zero in the tenths place. Now our division problem looks like 10 divided by 2, and that’s easy to do! The only difference is we have a decimal point. Let’s ignore the decimal point for a minute and pretend that our problem really is 10 divided by 2. So 2 will go into 10 five times because 5 times 2 equals 10, and that leaves no remainder. So we’redone, right? Not so fast, we’ve got that decimal point to deal with. And we know that 5 can’t be the answer because 5 is bigger than one-half. We just need to include the decimal point in our answer for it to be correct. We put it directly above the decimal point in our problem. There… now our answer is “point 5” (or 0.5 which is the more proper way to write it.) So, by dividing, we figured out that the decimal value of 1/2 is 0.5 Now let’s try converting the fraction 3/4 by dividing. Of course, we start by rewriting our fraction like this: 3 divided by 4. And again, we run into the same problem: 4 is too big to go into 3, so it looks like we’re going to need a decimal point here too. Let’s put a decimal point after the 3, and a zero in the tenths place to make 3.0 Now our problem almost looks like 30 divided by 4. Now if you remember your multiplication table, you’ll know that 4 goes into 30 seven times because 7 times 4 is 28. 30 minus 28 leaves a remainder of 2, but we don’t want a remainder, so let’s keep going. 4 is too big to divide into 2, so the only way we can get rid of the remainder is to use another zero in the hundredths place which make the number we’re dividing up kind of look like 300. Now we can bring down that extra zero to make the remainder look like 20. And 4 will go into 20 five times because 5 times 4 equals 20, and that leaves no remainder. Oh, yeah! But don’t forget, we need to include the decimal point in our answer. Now if you’ve kept...

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What is converting 0127repeating decimals to?

Converting 0127repeating decimals refers to the process of transforming a repeating decimal representation, such as 0.127127127..., into a simplified and concise form, such as 0.127.

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There is no specific requirement to file converting 0127repeating decimals, as it is a mathematical operation and not a form or report that needs to be filed.

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Converting 0127repeating decimals is a mathematical process and does not involve filling out any forms. It can be done using various techniques and algorithms taught in mathematics.

What is the purpose of converting 0127repeating decimals to?

The purpose of converting 0127repeating decimals is to simplify and express a repeating decimal number in a more concise and comprehensible form. It allows for easier calculations and comparisons.

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