The important question is what is a fraction. If the fractions exclude the integers, integers are not fractions. It is not about thinking about numbers in different ways. I'll assume by "fraction" you mean "rational number". If you want to be extremely pedantic , the answer is, in some sense, no. It would be pointless to so pedantic to say that integers are not rational numbers.
But, sometimes when doing math, I find it useful to switch between thinking of things as subsets, and thinking of things embedding into another thing, even when something isn't actually a subset. The set of rational numbers can be partitioned into the set of ratios and the set of integers. Five clearly falls into the second partition. So the question is, do you define "fraction" as "ratio" the first partition only or as "rational".
I would tend to agree with you and define fractions as being non-integral rational numbers, or ratios. If an integer is a fraction, that legitimizes nonsense like: 5 is 3, plus a fractional part of 2.
Also, note that we never say that numbers are divisible by 1. Prime numbers simply have no divisor, and two relatively prime integers have no common divisor, and that is that. The phrase "other than one" is added so that school children don't get excited. Oh, and by the way, I slipped today and fractured my leg.
Luckily, it was fractured in zero places so it is not actually broken. Each bone manifests itself in one whole, healthy fragment! Any integer is a rational number being that the definition of a rational number is any number that can be expressed as the ratio of two integers.
It is enough to have the property without having to explicitly express it as such. As far as the semantics go I would disagree and say that any integer is not a fraction. Any integer can be written as a fraction but until you write it in that format its an integer. Also, I see a lot of people mentioning that all fractions are rational numbers which is not true. Sign up to join this community.
The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Fractions and decimals are not included in the set of integers. The numbers such as 8. We can plot the integers as equally spaced points on a number line , as shown in the figure. The arrows at the left and right sides show that the integers continue forever in both directions.
The whole numbers greater than 0 are called positive integers. Their opposites, which are less than 0 , are called negative integers. We cannot say infinitely many digits! We can go in the reverse direction and change decimals to fractions, too! When we have a terminating decimal expansion, such as 4. The 2 of 4.
If we are starting with a repeating decimal, we have to do a bit more work to find its corresponding fraction. For example, consider 0. Call this number A. The repeating portion 35 has two digits, so we multiply A by to move the decimal over two places. Notice that all the decimal places in A and A match up. We subtract A from A to get 99 A.
When we subtract the decimals, the 0. Therefore, we are left with only whole numbers! For any repeating decimal, we can use the same process to find the corresponding fraction. We multiply by 10, , , or whatever is necessary to move the decimal point over far enough so that the decimal digits line up.
Then we subtract and use the result to find the corresponding fraction. This means that every repeating decimal is a rational number! What if we have a decimal expansion that does not end, but the digits do not repeat? For example, look at 0. In this number, we increase the number of 0s between each pair of 1s, first having one 0 between, then two 0s, then three 0s, etc.
This cannot be a rational number since we know the decimals for rational numbers either terminate or repeat. This is an example of an irrational number. An irrational number is any number that we can put on a number line that cannot be written as a fraction of whole numbers.
Going back to our game, all irrational and rational numbers together fill up our number line between 0 and 1. Suppose your friend Jordan could pick any number between 0 and 1 and chose an irrational number for you to guess.
You would likely have a very hard time guessing the number exactly! Just like with the repeating decimal expansion of 3 22 , you cannot say infinitely many digits, so this game seems very unfair. Let us change the game so you can win! Jordan chooses three things: a number for you to guess, a range of numbers in which that number lies, and how close your guess has to be.
Find a Tutor. Integer Definition An integer is a whole number from the set of negative, non-negative, and positive numbers. Here is a list of integers: - 9 0 25 - 7, Table Of Contents [hide] [show]. Avoid confusing the different groups of numbers with the different ways we represent them.
A set of integers is represented by the symbol Z. Zero plays a vital role on the number line. Learn more about the integer zero. What you learned: After working your way through this lesson and video, you have learned: The definition of whole numbers and how to find them. Integers are one of the many types of number systems.
Integers can be arranged into sets of numbers.
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