Mathematics: Repeated decimals can be written as an infinite geometric series to convert them to a fraction. consider the repeating decimal below. 0.232323… = 0.23 + 0.23(0.01) + 0.23(0.01)2 + … what is a1? what is r?

Repeated decimals can be written as an infinite

amar82

03.01.2022

a_1=0.23 and r=0.1 .

Step-by-step explanation:

It is given that Repeated decimals can be written as an infinite geometric series to help convert them to a fraction.

Consider the repeating decimal below.

0.232323…=0.23+0.23(0.01)+0.23(0.01)^2+…

We need to find the value of $a_1\text{ and }r$ .

a_1 is the first term of the series. So,

a_1=0.23

is the common ratio of the series. So,

$r=\dfrac{a_2}{a_1}=\dfrac{0.23(0.1)}{0.23}=0.1$

Therefore, a_1=0.23 and r=0.1 .

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tyrique86

27.05.2023

2x+18+5x-9

2x+5x18-9

7x+9

7. 7

x= 1.4

hope it helps

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