1.21 Repeating as a Fraction
What is 1.21 Repeating?
1.21 repeating, also written as 1.2121..., is a non-terminating decimal expansion that repeats in a cycle of two digits: 21. This type of decimal is called a repeating decimal or a recurring decimal.
Converting 1.21 Repeating to a Fraction
To convert a repeating decimal to a fraction, we can use the following steps:
Step 1: Let the repeating part of the decimal be equal to a variable, say x.
Step 2: Multiply both sides of the equation by a power of 10, such that the repeating part is shifted to the left of the decimal point. In this case, we multiply by 100.
Step 3: Subtract the original equation from the new equation to eliminate the non-repeating part of the decimal.
Step 4: Simplify the resulting equation to solve for x.
Let's apply these steps to convert 1.21 repeating to a fraction:
Step 1: Let x = 1.2121...
Step 2: Multiply both sides by 100:
100x = 121.2121...
Step 3: Subtract the original equation from the new equation:
99x = 120
Step 4: Solve for x:
x = 120/99
x = 40/33
Therefore, 1.21 repeating as a fraction is 40/33.
Remember that this fraction can be simplified or written in its lowest terms, but the result remains the same.
