Write .4(5) as a fraction.
The parenthesis represent it as a repeating decimal:
.455555555555555555555
But what is it in a fraction?
.4 + 5/100 + 5/1000 + 5/10,000.......
.4 + 5/100 +(5/100)(1/10) ..
.4 + infinite geometric series with a = 5/100 and r = 1/10
.4 + sum of series
.4 + a/(1-r)
.4 + 5/100 / (9/10)
4/10 + (5/9)/ 10
(4 5/9 )/10
41/90
my calculator says yes that works :)
thanks DAMON
You are welcome :)
To write .4(5) as a fraction, we first need to understand the notation being used. The .4(5) notation indicates that the digit 5 repeats infinitely after the decimal point.
To convert this repeating decimal into a fraction, we can follow these steps:
Step 1: Let x be the repeating decimal we want to convert.
Step 2: Multiply x by a power of 10 so that the repeating part is shifted to the left of the decimal point. In this case, we want to shift the repeating 5 to the left. Since there is only one repeating digit, we multiply x by 10:
10x = 4.5555555555...
Step 3: Subtract the original number from the shifted number to eliminate the repeating part:
10x - x = 4.5555555555... - 0.4555555555...
Simplifying the equation gives:
9x = 4.1
Step 4: Solve for x by dividing both sides of the equation by 9:
x = 4.1 / 9
Since we want to express x as a fraction, the division can be done as follows:
x = 41/90
Therefore, the fraction equivalent of .4(5) is 41/90.