How do you convert 0,5444444444 into a common fraction by first writing it as a geometric series...I tried it this way 0,5 (0,004+0,0004...)But it doesn't work out please help
Your decimals are not correct
0.5444444444
= .5 + .04 + .004 + .0004 + ...
let's leave the .5 sitting aside for the time being.
so we have
.04 + .004 + ...
a = .04, r = .1
sum of all = a/(1-r) = .04/(1-.1)
= .04/.9
= 4/90 = 2/45
now bring in the .5 or 1/2
so 0,5444444444
= 1/2 + 4/90
= 49/90
btw, that is not the easiest way to do this, but it was the method you needed.
Yes, I was confused, You put 0,5444444444. For future reference, use .'s
To convert the decimal number 0.5444444444 into a common fraction using a geometric series, we can follow these steps:
Step 1: Write the given decimal number as the first term of the geometric series.
The given decimal is 0.5444444444, so the first term of the series is 0.5444444444.
Step 2: Determine the common ratio of the geometric series.
The common ratio can be found by dividing any term of the series by its preceding term.
In this case, we can observe that each subsequent term is obtained by dividing the preceding term by 10 and adding 4.
For example:
0.0044444444 = 0.5444444444 / 10 + 4
0.0004444444 = 0.0044444444 / 10 + 4
Therefore, the common ratio is (1/10) + 4 = (41/10).
Step 3: Write the given decimal as a sum of an infinite geometric series.
We can use the formula for the sum of an infinite geometric series:
S = a / (1 - r)
where S is the sum, a is the first term, and r is the common ratio.
Plugging in the values:
S = 0.5444444444 / (1 - (41/10))
Step 4: Simplify the expression.
To simplify S, we need to find a common denominator for 1 and (41/10):
S = 0.5444444444 / (10/10 - (41/10))
= 0.5444444444 / ((10 - 41)/10)
= 0.5444444444 / (-31/10)
To divide by a fraction, we multiply by its reciprocal:
S = 0.5444444444 * (-10/31)
Step 5: Perform the calculation to obtain the final result.
We can evaluate the multiplication:
S = -0.1770324448
Therefore, the common fraction equivalent of the decimal 0.5444444444 using a geometric series is -0.1770324448.