Question

Write three numbers whose decimal expansions are non terminating non repeating


textbook:- NCERT textbooks
lesson name:- number system​

Answer 1

Answer:

Summary: The three numbers whose decimal expansions are non-terminating and non-recurring are 0.21221222..., 0.03003000300003... and 0.825882588825....

Answer 2

CONCEPT :

The Terminating numbers are those which when converted to decimal expansion then the number of digits after decimal point are finite, like 1.732 is a terminating number but 1.7325698357203803832………. is non-terminating number. Now recurring numbers are those which when converted to decimal number then the digits of the number on the right of the decimal point repeats after a regular interval. Like 3.2¯3¯

= 3.232323232323…….. is a recurring number because 23 repeats after the decimal point but 3.23436782443….. is a non-recurring number.

SOLUTION :

The Decimal expansion of any number means that when we change the number to decimal number or decimal point is involved in the number. Like 1/2 is a fractional number but when we change it to decimal then we completely divide the numerator by denominator. So, decimal expansion of 1/2 will be 0.5

we know that, rational numbers are those numbers that either terminate or if they are non-terminating then they are recurring numbers or digits of the number after decimal points repeat after a fixed period.

:$\implies$But the irrational numbers are non-terminating and non-recurring numbers.

:$\implies$So, we had to write three irrational numbers.

So, examples of irrational numbers are √2 ,π and √3

:$\implies$Now let us change them to decimal expansion.

So, decimal expansion of √2 is

:$\implies$1.414213562373095……….

Decimal expansion of √3

:$\implies$1.7320508075688…….

And decimal expansion of π

is 3.141592653589…….

Hence, decimal expansion of √2 , π and √3 are non-terminating and non-recurring.

Hope it's helps ^-^