# Write a rational number as a decimal

Mixed number to decimal calculator finds the decimal equivalent by converting a mixed number, fraction, integer or whole number to a decimal. How to Convert a Mixed Number to a Decimal Follow these 2 steps to convert a mixed number to a decimal: Math Home Search Dr. Repeating decimals to fractions Hello, I was asked this question the other day and I could not remember how to convert a repeating decimal into a fraction. For example, I know. Repeating decimals to fractions Hello, Oscar As you may already know, every fraction technically, a fraction is called a rational number either terminates - ends with a string of 0's - or is a repeating decimal of course, you could think of the string of zeros as just a special kind of repeating decimal.

The decimals that neither terminate nor repeat cannot be repreented by fractions with integers on the top and bottomand are called "irrational" numbers. So the question that occurs, as it did to you, is how to find out what fraction that repeating decimal is equal to.

And you're right, there is a trick to it. Suppose that you have a repeating decimal, and it looks like. Oh yes, the trick First, you have to count the number of digits in the repetend.

When a is 3, the number of digits is 1, when a is 09, the number of digits is 2, and when a isthe number of digits is 6. Now, multiply your repeating decimal by a power of 10, namely, the power of 10 which is a 1 followed by a number of zeros equal to the number of digits in the repetend.

That's a mouthful, so let's see how it works in the examples above: If we multiply the repeating decimal by a power of 10 in this way, we end up with a decimal which has the repetend to the LEFT of the decimal point, and the same repeating decimal we started out with to the RIGHT of the decimal point: But now note that after we multiply by this appropriate power of 10, we get the sum of an integer which is numerically equal to whatever the repetend was and the repeating decimal we started out with. If we let x be the repeating decimal we started out with, we find: So now that you feel you understand this, let me throw a monkeywrench into the whole thing: If we looked at 0. Couldn't it just as well be 33, oror even ?

The answer is that it could, but and this takes a little more work it ends up giving you the same fraction after reduction to lowest terms. The study of repeating decimals is an interesting one, and there are many deep and interesting questions one can ask about them.

Let me leave you with one of these. But if you go into the library and look up any book on Number Theory, it's explained there.Rational Numbers Write each fraction or mixed number as a decimal.

Use a bar to show a repeating decimal. Session 7 Fractions and Decimals Key Terms in This Session Previously Introduced Write and Reflect Problem A8. Is the converse of that statement true? That is, is every terminating or repeating decimal a rational number? The answer is yes.

And any non-terminating, non-repeating decimal cannot be a rational number. The definition says that a number is rational if you can write it in a form a/b where a and b are integers, and b is not r-bridal.comy all fractions are of that form, so fractions are rational numbers.

Terminating decimal numbers can also easily be written in that form: for example = 67/, = /, and so on. A fraction a/b (in its lowest terms) is a terminating decimal only when its denominator that is b can be expressed Worksheet on Rational Number as Decimal Numbers Practice the questions given in the worksheet on rational number as decimal numbers.

1 7/16 is a mixed number that is a number between 1 and 2. 1 is the whole number. 7/16 is a fraction that is added to a whole number.

 Rational Numbers Developing the Concept Real Numbers:

So we convert the fraction part to a decimal. Any rational number can be written as a decimal fraction, including integers. is an example of an decimal integer written as a decimal fraction. k Views.

Expressing rational numbers as decimals worksheet