Q3 of 24 Page 50

Express the following decimal expansions into rational numbers.

i. ii.


iii. iv.


v. vi.

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



More from this chapter

All 24 →
1

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

i. ii.


iii. iv.


v. vi.


vii. viii.

2

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

i. ii.


iii. iv.

4

Explain in decimal form. Find the number of digits in the repeating block.

 5

Find the decimal expansions of and by division method. Without using the long division method, deduce the decimal expressions of from the decimal expansion of .