Hong Kong
Stage 4 - Stage 5

# Applications of Geometric Series

## Interactive practice questions

The recurring decimal $0.8888\dots$0.8888 can be expressed as a fraction when viewed as an infinite geometric series.

a

Express the first decimal place, $0.8$0.8 as an unsimplified fraction.

b

Express the second decimal place, $0.08$0.08 as an unsimplified fraction.

c

Hence write, using fractions, the first five terms of the geometric sequence representing $0.8888\dots$0.8888

d

State the values of $a$a, the first term, and $r$r, the common ratio, of this sequence.

$a$a$=$=$\editable{}$

$r$r$=$=$\editable{}$

e

If we add up infinitely many terms of this sequence, we will have the fraction equivalent of our recurring decimal. Calculate the infinite sum of the sequence as a fraction.

Easy
4min

The decimal $0.6666$0.6666$...$... can be expressed as a fraction.

Easy
1min

The recurring decimal $0.444444\dots$0.444444 can be expressed as a fraction when viewed as an infinite geometric series.

Easy
3min

Consider the number $0.252525$0.252525$\ldots$

Easy
1min