which can be expressed as a simple fraction
A. 3.6363636363...
or
B. 52.781654292
A. 3.6363636363...
This can be expressed as a simple fraction. The infinite repeating decimal can be written as 3.(63), where the digits in parentheses repeat infinitely. To convert this to a fraction, we let x = 3.(63) and multiply both sides by 100, so 100x = 363.(63). Then, we subtract the equation 100x = 3.(63) from 100x = 363.(63) to eliminate the decimal part. This gives us:
100x - x = 363.(63) - 3.(63)
99x = 360
x = 360/99
Therefore, 3.(63) can be expressed as the fraction 360/99, which simplifies to 40/11.
Thus, A. 3.6363636363... can be expressed as the simple fraction 40/11.
what about b
B. 52.781654292
This number cannot be expressed as a simple fraction because it is a non-repeating decimal. It is a finite decimal with many decimal places and does not have a pattern to repeat. As such, it cannot be represented as a fraction with whole numbers in the numerator and denominator.
The number that can be expressed as a simple fraction is A. 3.6363636363...
To express this as a fraction, we can start by letting x = 3.6363636363...
We can then multiply both sides of the equation by 100 to eliminate the decimal places: 100x = 363.63636363...
Next, we subtract the original equation (x = 3.6363636363...) from this new equation (100x = 363.63636363...):
100x - x = 363.63636363... - 3.6363636363...
Simplifying both sides gives us:
99x = 360
Finally, dividing both sides of the equation by 99 gives us the fraction equivalent of the decimal:
x = 360/99
Therefore, the number 3.6363636363... can be expressed as a simple fraction: 360/99.