Question

which geometric series represents 0.4444... as a fraction? a) 1/4, 1/40, 1/400, 1/4,000 b) 1/40, 1/400, 1/4,000, 1/40,000 c) 4/10, 4/100, 4/1,000, 4/10,00 d) 1/10, 1/100, 1/1000, 1/10000

Answer 1

The answer is c) 4/10, 4/100, 4/1,000, 4/10,00

Answer 2

Answer:
`(4)/(10)+(4)/(100)+(4)/(1,000)+(4)/(10,000)`

Explanation:

The given geometric series are:

a)
`(1)/(4)+(1)/(40)+(1)/(400)+(1)/(4,000)`

on simplifying in decimals, we get

`0.25+0.025+0.0025+0.00025=0.27775\\eq0.4444`

b)
`(1)/(40)+(1)/(400)+(1)/(4,000)+(1)/(40,000)`

on simplifying in decimals, we get

`0.025+0.0025+0.00025+0.000025=0.027775\\eq0.4444`

c)
`(4)/(10)+(4)/(100)+(4)/(1,000)+(4)/(10,000)`

on simplifying in decimals, we get

`0.4+0.04+0.004+0.0004=0.4444`

Thus, this geometric series represent 0.4444.

d)
`(1)/(10)+(1)/(100)+(1)/(1,000)+(1)/(10,000)`

on simplifying in decimals, we get

`0.1+0.01+0.001+0.0001=0.1111\ \\eq0.4444`