There are infinite numbers between two rational numbers,the numbers can be even in fraction form. Explain in detail with other numbers .
There are infinite numbers between two rational numbers,the numbers can be even in fraction form. Explain in detail with other numbers .
We can insert infinitely many rational numbers between any two rational numbers. This property of rational numbers is known as the dense property.
How to find out some rational numbers lying between two given rational numbers, say between -4/7 and 2/7. The four rational numbers -3/7, -2/7, -1/7, 0/7 and 1/7 lies between -4/7 and 2/7.
Wecan apply the same procedure to insert more rational numbers between -4/7 and 2/7.
The rational numbers -4/7 and 2/7 can also be written as -40/70 and 20/70 respectively.
Clearly, -39/70, -38/70, -37/70, -36/70, -35/70, …….., 0/70, 1/70, 2/70, 3/70, 4/70, …….., 18/70, 19/70 are rational numbers between -4/7 and 2/7.
The total number of these rational numbers is same as the number of integers between -40 and 70, i.e., 70 - (-40) - 1 = 70 + 40 - 1 = 110 - 1 = 109.
Similarly, by re-writing -4/7 and 2/7 as -400/700 and 200/700, we can insert 700 - (-400) - 1 = 700 + 400 - 1 = 1100 - 1 = 1099 rational numbers between -4/7 and 2/7.
Therefore, we can apply the same procedure to insert as many rational numbers between -4/7 and 2/7.
We can insert infinitely many rational numbers between any two rational numbers. This property of rational numbers is known as the dense property.
How to find out some rational numbers lying between two given rational numbers, say between -4/7 and 2/7. The four rational numbers -3/7, -2/7, -1/7, 0/7 and 1/7 lies between -4/7 and 2/7.
Wecan apply the same procedure to insert more rational numbers between -4/7 and 2/7.
The rational numbers -4/7 and 2/7 can also be written as -40/70 and 20/70 respectively.
Clearly, -39/70, -38/70, -37/70, -36/70, -35/70, …….., 0/70, 1/70, 2/70, 3/70, 4/70, …….., 18/70, 19/70 are rational numbers between -4/7 and 2/7.
The total number of these rational numbers is same as the number of integers between -40 and 70, i.e., 70 - (-40) - 1 = 70 + 40 - 1 = 110 - 1 = 109.
Similarly, by re-writing -4/7 and 2/7 as -400/700 and 200/700, we can insert 700 - (-400) - 1 = 700 + 400 - 1 = 1100 - 1 = 1099 rational numbers between -4/7 and 2/7.
Therefore, we can apply the same procedure to insert as many rational numbers between -4/7 and 2/7.
has the smallest element.