what the decimals end behavior to Changing a repeating decimal to a fraction - RATIONAL.
The end behavior of changing a repeating decimal to a fraction is that the fraction will always be a rational number. This is because a repeating decimal can be expressed as a fraction where the repeating part of the decimal becomes the numerator and the denominator is the number of digits being repeated. Therefore, by converting a repeating decimal to a fraction, we are essentially representing the number as a ratio of two integers, which is a characteristic of a rational number.
examples?
Sure! Here are some examples of converting repeating decimals to fractions:
1. 0.333... (repeating 3's)
To convert this to a fraction, let x = 0.333...
Multiply both sides by 10 to move the decimal point:
10x = 3.333...
Now subtract the original equation from the new equation:
10x - x = 3.333... - 0.333...
9x = 3
x = 3/9 = 1/3
Therefore, 0.333... = 1/3
2. 0.727272... (repeating 72's)
Let x = 0.727272...
Multiply both sides by 100 to move the decimal point:
100x = 72.727272...
Now subtract the original equation from the new equation:
100x - x = 72.727272... - 0.727272...
99x = 72
x = 72/99 = 8/11
Therefore, 0.727272... = 8/11
These are examples of how repeating decimals can be converted to fractions, which are rational numbers.