Express 4.050505... as a fraction
let x = 4.050505...
multiply by 100, (since the length of the repeating loop is 2 , had it been 4, I would have multiplied by 10000)
100x = 405.0505...
subtract:
99x = 401.000.. = 401
x = 401/99
it is 2 digit repeating ... so multiply by 100 ... then subtract ... and divide
n = 4.050505... , 100 n = 405.050505...
99 n = 401
To express 4.050505... as a fraction, we can follow these steps:
Step 1: Let x = 4.050505...
Step 2: Multiply both sides of the equation by 1000 to eliminate the decimal:
1000x = 4050.505...
Step 3: Subtract x from both sides of the equation to eliminate the repeating decimal:
1000x - x = 4050.505... - 4.050505...
999x = 4046.4545...
Step 4: Multiply both sides of the equation by 1/999 to isolate x:
x = (4046.4545...)/999
Step 5: Simplify the fraction, using a calculator or long division:
x = 4 040 / 999
Thus, 4.050505... can be expressed as the fraction 4 040/999.
To express 4.050505... as a fraction, we can use the concept of infinite geometric series.
Let's call x = 4.050505...
Now, we can multiply x by 10000 to eliminate the decimal point:
10000x = 40505.050505...
Next, let's subtract the original x from the new equation:
10000x - x = 40505.050505... - 4.050505...
9999x = 40501
To solve for x, divide both sides of the equation by 9999:
x = 40501 / 9999
This fraction, 40501/9999, is the expression of 4.050505... as a fraction.