Explain why $3. ¯ ¯¯¯¯¯¯¯¯¯ ¯ 1416$ is a rational number.

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Solution

$3. ¯ ¯¯¯¯¯¯¯¯¯ ¯ 1416$ is a rational number because we can write it in the form of $\frac{p}{q}$ , where q $\neq$ 0. Apart from this the given decimal number has recurring number 1416, hence it is a rational number.

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Similar questions

Q. Explain why

3 . \bar{1416}

is a rational number.

Classify the following numbers as rational or irrational:

$(i) \frac{22}{7} (i i) 3.1416 (i i i) π (i v) 3. ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 142857 (v) 5.636363... (v i) 2.040040004... (v i i i) 1.535335333.... (v i i i) 3.121221222... (i x) \sqrt{21} (x) \sqrt[3]{3}$

Q. Which of the following is an irrational number?

(a)

\frac{22}{7}

(b) 3.1416
(c)

3.1416

(d) 3.141141114...

Which of the following is a rational number and explain why :

1.Root 2

2. 0(zero)

3. Root 4

4. Root of -16

Q. Classify the following numbers as rational or irrational:

(i)

\frac{22}{7}

(ii) 3.1416
(iii) π
(iv)

3.142857

(v) 5.636363...
(vi) 2.040040004...
(vii) 1.535335333...
(viii) 3.121221222...
(ix)

\sqrt{21}

(x)

\sqrt[3]{3}

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Explain why 3.¯¯¯¯¯¯¯¯¯¯¯1416 is a rational number.

3.¯¯¯¯¯¯¯¯¯¯¯1416 is a rational number because we can write it in the form of pq, where q ≠ 0. Apart from this the given decimal number has recurring number 1416, hence it is a rational number.

Explain why $3. ¯ ¯¯¯¯¯¯¯¯¯ ¯ 1416$ is a rational number.

$3. ¯ ¯¯¯¯¯¯¯¯¯ ¯ 1416$ is a rational number because we can write it in the form of $\frac{p}{q}$ , where q $\neq$ 0. Apart from this the given decimal number has recurring number 1416, hence it is a rational number.