Question

The value of 0.5454... is (using short cut) *​

Answer 1

Answer:

yrufuhvgueuufycdhyeufyyydyeydyyfhf

Answer 2

Step-by-step explanation:

Let

x

=

0

.

¯¯¯¯

54

⇒

100

x

=

54

.

¯¯¯¯

54

⇒

100

x

−

x

=

54

.

¯¯¯¯

54

−

0

.

¯¯¯¯

54

⇒

99

x

=

54

⇒

x

=

54

99

=

6

11

This strategy works in general. Given a repeating decimal, let

x

represent the initial value, multiply by

10

n

where

n

is the number of digits repeating, subtract

x

(the original value), and solve for

x

.

We can also notice a pattern in the above: we always end up with the repeating portion divided by

10

n

−

1

, where

n

is the number of digits in the repeating portion. This gives us a shortcut:

0

.