Anyone know what 1.27 repeating is as a fraction??
The correct answer and explanation is:
The number 1.27 repeating, written as 1.272727…, means the digits “27” repeat infinitely after the decimal point. To convert this repeating decimal into a fraction, follow these steps:
First, let x=1.272727…x = 1.272727….
Since “27” is the repeating block of two digits, multiply xx by 100 to shift the decimal point two places to the right: 100x=127.272727…100x = 127.272727…
Now subtract the original xx from this equation: 100x−x=127.272727…−1.272727…100x – x = 127.272727… – 1.272727… 99x=12699x = 126
Here, the repeating parts after the decimal cancel out because they are the same on both sides.
Next, solve for xx: x=12699x = \frac{126}{99}
This fraction can be simplified by dividing numerator and denominator by their greatest common divisor, which is 9: 126÷999÷9=1411\frac{126 \div 9}{99 \div 9} = \frac{14}{11}
So, the fraction equivalent to 1.27 repeating is 1411\frac{14}{11}.
To check, divide 14 by 11: 14÷11=1.272727…14 \div 11 = 1.272727…
which matches the original repeating decimal.
Explanation:
Repeating decimals represent fractions with denominators related to powers of 10 minus 1, depending on the length of the repeating block. In this case, the repeating block “27” has two digits, so multiplying by 100 aligns the decimals properly for subtraction. This subtraction removes the infinite repeating portion, leaving an equation with whole numbers that can be solved for the variable representing the decimal. Simplifying the resulting fraction ensures it is in its simplest form. This method is a standard way to convert any repeating decimal into a fraction.