# How to write a rational number as a repeating decimal

Question from lil, a student: Why are repeating decimals considered rational numbers? We have two responses for you Hi Lil, The answer is yes, but before I illustrate why I am going to quibble with the way you asked the question. July 28, at 5: Can 0 be infinite in an infinite sequence of numbers? In order for 0 to repeat itself infinitely, it must have an infinitely small amount of numbers prior to it, meaning that each digit is a representation of its own infinity.

However, no number IS 0. All numbers are the byproduct of 0, the period of time. Therefore, it is impossible… Julia September 20, at 1: This is an important distinction.

You have to consider units. That value for the plank length you have quoted is in meters-an entirely arbitrary human unit. If you did want to use the physical world to set a limit on the digits of pi, then you would use a ratio. This number would be far smaller than the plank length in meters.

But it would still put a limit on physically meaningful digits of pi. But what if that is not the smallest physical ratio? Why stop at the edge of the observable universe?

There is no reason think it stops there. If, indeed, the universe is physically infinite, then the smallest physical ratio approaches 0, so you can have as many digits of pi as you like and they are still within the range of physically relevant numbers. The important point is that while the Plank length is definitely a distance, Pi is definitely not. Moote September 20, at 1: Perhaps I did not discuss that but I had intended to. This is exactly what I was talking about. Not number theories on paper or a chalkboard. Assuming Planck was correct in his theory I entirely was referring to the physical world when i posted that.

In the real world number have no meaning if they cannot be applied to something real.In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of metin2sell.com the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable, meaning that they share no .

Terminating*andRepeating*Decimals* * * * * Student’Probe’’ Write* *as*adecimal.* * Answer* * LessonDescription* In*this*lesson*students*use*long*division. Rational Numbers 9: Decimal Form of Rational Numbers There are often several different ways to model a given decimal number, depending on which type of block is selected to represent 1.

For Suppose that the fraction 1/n is represented by a repeating decimal. What, if anything, can you say about the fractions 2/n, 3/n, 4/n, etc? 5. Write each rational number as a repeating decimal. 4. 7 9 5. 11 15 6. 8 Write a mixed number that has a repeating decimal, and write the decimal.

_____ The ruler is marked at every 1 16 inch.

## What Is a Rational Number?

Do the labeled measurements convert to repeating or terminating decimals?. This means that after a certain number of decimal places (let's call that k), the decimal begins repeating every h digits, where h is some integer. For example, if the number . use a calculator to find the decimal form of the rational number.

if it is a nonterminating decimal, write the repeating pattern. algebra i need you to check my answers for the following questions: use the table to answer problems 1 to 4. the table lists the commuting times for 5 people. write each ratio in the form a/b, and then as a decimal. Intro to rational & irrational numbers | Algebra (video) | Khan Academy