Q. 34.8( 4 Votes )

Find three rational numbers lying between 0 and 0.1. Find twenty rational numbers between 0 an 0.1. Give a method to determine any number of rational numbers between 0 and 0.1.

Answer :

To determine any number of rational numbers between 0 and 0.1 insert 0 after the decimal and any digit between 1-9 after that.

Insert 0 after decimal and then 1 =0.01

Insert 0 after decimal and then 5 =0.05

Insert 0 after decimal and then 9 =0.09

The three rational numbers lying between 0 and 0.1 are-

0.01, 0.05, 0.09.

Insert double zero after decimal and then 1 = 0.001

and further appending numbers between in sequence i.e. 0.002,0.003,0.004,0.005,0.006 ……

The twenty rational numbers between 0 and 0.1 are-

0.001                0.002                0.003                0.004        0.005

0.006                0.007                0.008                0.009        0.010

0.011                0.012                0.013                0.014        0.015

0.016                0.017                0.018                0.019        0.020

And now we can find rational numbers between any two numbers. For Example rational numbers between 0.1 and 0.2

We just need to make one extra digit after 0.1 and we can get any number of rational numbers.

So, rational numbers between 0.1 and 0.2 are

0.11, 0.12, 0.13, 0.14, 0.15, 0.16........

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