Can integers be fractions

Integers include all whole numbers, plus the negatives of all the numbers except zero. They do not include any decimal or fractional numbers. Fractions, on the other hand, express one integer divided by another, and often equal a decimal number.

Because of this, not all fractions can be turned into integers by merely completing the division. When a fraction appears as part of an equation, however, you can multiply the whole equation by the inverse of the fraction or a multiple of the inverse to turn the fraction into an integer. If you are playing the guess-the-number game, you can arrive at this decimal version of 7 16 in several short steps. The table below shows a possible way this could happen.

In the table, H means your guess was too high and L means your guess was too low. Because the decimal for the number 7 16 ends, you can get the exact number by guessing one digit at a time in the decimal. Does this happen for all fractions? Let us look at the decimal for 3 Following the same division process, we get a 1 on top with a remainder of 8, a 3 on top with a remainder of 14, a 6 on top with a remainder of 8, a 3 on top with a remainder of 14 … but wait!

We have already seen these remainders, and we know that the next number on top is a 6 with a remainder of 14 again. This means that if you try to guess the number 3 22 one decimal place at a time, you will be guessing forever!

All of the numbers we have considered so far are called rational numbers. A rational number is any number that we can write as a fraction a b of two integers whole numbers or their negatives , a and b.

This means that 2 5 is a rational number since 2 and 5 are integers. Even if we do not write 3 and 4. We have seen that some rational numbers, such as 7 16 , have decimal expansions that end. We call these numbers terminating decimals. Other rational numbers, such as 3 22 , have decimal expansions that keep going forever. But we do know that even the decimal expansions that do not terminate repeat, so we call them repeating decimals. For example, when we were changing 3 22 into a decimal, the only options we had for remainders were 0, 1, 2, 3, …, 20, Because there are only a finite number of remainders, the remainders must start to repeat eventually.

This is true for all fractions whose decimals do not terminate. Even though there is a repeating pattern to the decimals for these fractions, we will never guess the exact number in the guessing game if we are guessing one decimal place at a time because the decimal goes on forever. 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. Your subscribed friend will also get 1 month subscription absolutely free. Ask Your Doubts We are really eager to clarify your doubts.

Join Now. Company About Us. Our Team. Our Faculty. Behind the Scene. Zero is not considered a "natural number. The whole numbers are the numbers 0, 1, 2, 3, 4, and so on the natural numbers and zero. Negative numbers are not considered "whole numbers. The integers are Fractions and decimals are not integers. All whole numbers are integers and all natural numbers are integers , but not all integers are whole numbers or natural numbers.

For example, -5 is an integer but not a whole number or a natural number.