Are repeating decimals infinite?

A repeating decimal or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely repeated portion is not zero. The infinitely repeated digit sequence is called the repetend or reptend.

Are repeating decimals bigger?

Would a repeating decimal be bigger than a regular decimal? – Quora. Given a Real number with a nonrepeating decimal representation, there is always a larger Real number with a repeating decimal representation, formed by adding repeated digits after the last digit of the given number.

What is the largest repeating decimal?

The largest repeating decimal part I was able to create so far was 1/97 which equaled 0. [01030927 83505154 63917525 77319587 62886597 93814432 98969072 16494845 36082474 22680412 37113402 06185567] (96 repeating digits).

What is the rule for repeating decimals?

The rule states that the period of a repeating decimal should be written first in the numerator of an ordinary fraction. And the denominator must contain some number of nines. In this case, the number of nines must be equal to the number of digits in the period of the repeating decimal 0.

Is an infinite decimal irrational?

Having an infinite decimal expansion is not what makes a number irrational. A rational number is any number that can be expressed as a fraction – that is, the words rational number and fraction are essentially synonymous.

Is decimals bigger than whole numbers?

As discussed in the concept of whole and decimal numbers, One can guess now which number must be bigger or which one must be smaller. If the whole number and decimal number before the decimal are equal, then the decimal number is bigger.

Is a repeating decimal irrational?

Numbers with a repeating pattern of decimals are rational because when you put them into fractional form, both the numerator a and denominator b become non-fractional whole numbers. This is because the repeating part of this decimal no longer appears as a decimal in rational number form.

Are repeating decimals irrational?

What is the longest possible repeating decimal part?

I know the repeating decimal part can’t exceed the denominator – 1. So the longest possible repeating decimal part has to be 9,998 or less. The reason I want to know is to test an algorithm that I wrote which accepts fractions with numerators and denominators up to 9,999.

What happens when you divide by an infinitely repeating number?

When division results in an infinitely repeating number, the number obviously gets truncated to fit into the size of the decimal. So something like 1/3 becomes something like 0.3333333333333333333….

How do you find the real number with a repeating decimal?

Given a Real number with a nonrepeating decimal representation, there is always a smaller Real number with a repeating decimal representation, formed by subtracting repeated digits after the last digit of the given number.

What is the longest Division that can be done with decimals?

So, the final answer to your question is that the longest repetend that can be obtained in a division between 2 integers smaller than 10,000 is 9966 decimals long. Any fraction of the form d/9967 will have a repetend this long if d is a non-zero integer that is not a multiple of 9967 – because… negative numbers.