Question

Do all real numbers have a decimal expansion? Select each correct answer. Some numbers, such as 1 10 ​, have a decimal expansion that terminates. All real numbers have a decimal expansion. Some numbers, such as 13 − − √ , do not have a decimal expansion. Only some real numbers have a decimal expansion. Some numbers, such as 1 18 ​, have a decimal expansion that repeats but does not terminate

Answer 1

Yes, All Real Nos. have Decimal Expansion.

Correct Options are :

Option A : Some nos. , sucha as
`(1)/(10)`. have a decimal expansion that terminates.

Option B : All Real Nos. have a decimal expansion.

Option E : Some nos. , such as
`(1)/(18)`, have a decimal expansion that repeats but does not terminate.

Explanation:

Real Number consist of Rational Numbers and Irrational Numbers.

Rational Nos. have 2 type of Decimal Expansion which are terminating and non terminating but repeating.

`(4)/(2)=2.0\:,\;(1)/(10)=0.1\:,\:(1)/(4)=0.25` are some example of terminating decial expansion.

`(1)/(3)=0.333333...\:=\;0.\overline{3}\:,\:(1)/(18)=0.0555555...\:=\:0.0\overline{5}` are some examples of non terinating but repeating decimal expansions.

Irrational Nos. have non terminating non repeating decimal expansions.

`√(2),√(3), so\:on\:, 0.1011001110001111000...\:, \:\pi` are some examples of non terminating non repeating decimal expansions.

Therefore, ALL Real Nos. have Decimal Expansion.

Correct Options are :

Option A : Some nos. , sucha as
`(1)/(10)`. have a decimal expansion that terminates.

Option B : All Real Nos. have a decimal expansion.

Option E : Some nos. , such as
`(1)/(18)`, have a decimal expansion that repeats but does not terminate.