Q. 3

# Express the following decimal expansions into rational numbers.

i. ii.

iii. iv.

v. vi.

Answer :

i. let

⇒ 100x = 18.181818 … = 18 + 0.181818…

⇒ 100x = 18 + x

⇒ 99x = 18

ii. let

⇒ 1000x = 427.427427 … = 18 + 0.427427427…

⇒ 1000x = 427 + x

⇒ 999x = 427

iii. let

⇒ 10000x = 1.00010001 … = 1 + 0.00010001…

⇒ 10000x = 1 + x

⇒ 9999x = 1

iv. As,

Let x = 0.454545…

⇒ 1 + x = 1 + 0.454545..

⇒ 1+ x = 1.45454545

⇒ 100 + 100x = 145.454545… = 145 + 0.454545…

⇒ 100 + 100x = 145 + x

⇒ 99x = 45

And

v. As,

Let x = 0.3333…

⇒ 7 + x = 7 + 0.3333…

⇒ 7 + x = 7.3333…

⇒ 70 + 10x = 73.3333… = 73 + 0.3333…

⇒ 70 + 10x = 73 + x

⇒ 9x = 3

And

vi. let

⇒ 1000x = 416.416416 … = 416 + 0.416416…

⇒ 1000x = 416 + x

⇒ 999x = 416

Rate this question :

Without actual division, find which of the following rational numbers have terminating decimal expansion.

i. ii.

iii. iv.

Tamilnadu Board Math Term-IWrite the following numbers in decimal form.

3.25 × 10^{-6}

Obtain the equivalent exponential form of the following.

Tamilnadu Board Math Term-III

Find the value of the following

Tamilnadu Board Math Term-III

Write the following numbers in decimal form.

1.86 × 10^{7}

Solve the following equations.

Tamilnadu Board Math Term-III

Convert the following rational numbers into decimals and state the kind of decimal expansion.

i. ii.

iii. iv.

v. vi.

vii. viii.

Tamilnadu Board Math Term-IObtain the equivalent logarithmic form of the following.

3^{5} = 243

Prove the following equations.

Tamilnadu Board Math Term-III

Prove the following equations.

log_{5}0.00125 = 3 - 5log_{5}10