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Answered 2014-09-02 01:17:04

Yes, that's what "repeating" refers to.

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Repeating decimals are ALWAYS rational numbers.

Yes. All numbers are rational numbers except repeating decimals like 1.3(repeating). * * * * * Repeating decimals are also rationals. However, the quotient is not defined if the second number is the integer zero!

Repeating decimals are always rational.

There are are three types of decimals: terminating, repeating and non-terminating/non-repeating. The first two are rational, the third is not.

Yes, terminating decimals are always rational numbers.

If you consider terminating decimals as ones that end in repeating 0s, then the answer is "always".

You can always convert a fraction to a decimal. For some fractions, you'll get terminating decimals. For example, 1/8 = 0.125. For other fractions, you get repeating decimals, such as 1/7 = 0.142857 142857 142857...To convert the fraction to a decimal, just divide the numerator by the denominator, for example on a calculator.

In fact, the statement is true. Consequently, there is not a proper counterexample. The fallacy is in asserting that a terminating decimal is not a repeating decimal. First, there is the trivial argument that any terminating decimal can be written with a repeating string of trailing zeros. But, Cantor or Dedekind (I can't remember which) proved that any terminating decimal can also be expressed as a repeating decimal. For example, 2.35 can be written as 2.3499... Or 150,000 as 149,999.99... Thus, a terminating decimal becomes a recurring decimal. As a consequence, all real numbers can be expressed as infinite decimals. And that proves closure under addition.

Yes - you can always convert numbers to scientific notation - whether they're whole numbers, or decimals.

It depends on what numbers you are multiplying and how many decimals places they each have. It doesn't always haveto move to the right.

Yes, because a fraction a/b where a and b are integer, and b is different than 0, is a rational number which are whole numbers or decimal numbers, where the decimal part is finite or repeating blocks. Conversely, decimals that do not repeat or terminate cannot be represented as a fraction. For example, in a right isosceles triangle with side a and hypotenuse (square root of 2)a, we can't represent as a fraction [(square root of2)a]/a (hypotenuse/side), because will have an irrational number (square root of 2). Here is one fun thing to know about repeating decimals. If you look at the repeating decimals formed by taking 1/n, where n is a prime number that is not 2 or 5, you will see that the length of the (smallest choice of) the part that repeats [i.e., 3, not 333, for 0.3333...] is: 1.always less than or equal to n-1, 2. equal to n-1 only for some of these prime numbers. 3. always a divisor of n-1.

When adding numbers with decimals always make sure the decimal points are lined up. That is the only way to be sure that the person will be adding them up right.

Decimals can be positive or negative.

We human beings are constantly looking for meaningful patterns in our environment, which is a fundamental technique by which we understand the world in which we live. However, we are not always successful in distinguishing between meaningful patterns and meaningless patterns. Numbers, and the many mathematical techniques that can be applied to numbers, yield an endless number of patterns. When we ascribe supernatural meaning to those patterns, we have numerology.

Yes. The square of an integer is just the number times itself. For any two whole numbers that are multiplied, the answer is always an integer (i.e. no decimals).

because you can always add a 0 when using decimals

The sum of two decimal numbers greater than 0.5 will always be greater than 1

§ In comparing two whole numbers, the one with the most digits is always the greater number. § In decimals the number with the greatest number of digits is not always the greatest.

Rangoli patterns are used in Diwali and they are always symmetrical.

No. Repeating decimals are always rational. 0.7777... is actually the decimal expansion of 7/9, which as you can clearly see is rational (it's the ratio of 7 to 9).