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

Answer: $\frac{4}{10}+\frac{4}{100}+\frac{4}{1,000}+\frac{4}{10,000}$

Step-by-step explanation:

The given geometric series are:

a)$\frac{1}{4}+\frac{1}{40}+\frac{1}{400}+\frac{1}{4,000}$

on simplifying in decimals, we get

$0.25+0.025+0.0025+0.00025=0.27775\neq0.4444$

b) $\frac{1}{40}+\frac{1}{400}+\frac{1}{4,000}+\frac{1}{40,000}$

on simplifying in decimals, we get

$0.025+0.0025+0.00025+0.000025=0.027775\neq0.4444$

c)$\frac{4}{10}+\frac{4}{100}+\frac{4}{1,000}+\frac{4}{10,000}$

on simplifying in decimals, we get

$0.4+0.04+0.004+0.0004=0.4444$

Thus, this geometric series represent 0.4444.

d)$\frac{1}{10}+\frac{1}{100}+\frac{1}{1,000}+\frac{1}{10,000}$

on simplifying in decimals, we get

$0.1+0.01+0.001+0.0001=0.1111\ \neq0.4444$

Answer 2

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