Reviewed by Jessica Kaminski
What is 0.3 repeating as a Fraction?
Answer: 0.3 repeating as a fraction is 1/3
The decimal 0.3 repeating (written as 0.333...) is a repeating, non-terminating decimal. Converting repeating decimals into fractions is a crucial skill in mathematics, helping to represent decimals exactly using ratios of integers.
Methods
Math Tutor Explanation Using Algebraic Method
One of the most common ways to convert a repeating decimal to a fraction is by using a simple algebraic method. This method uses a variable and simple equation to isolate the repeating decimal and solve for its fractional form.
Step 1: Step 1: Let x = 0.333...
Step 2: Step 2: Multiply both sides by 10 to get 10x = 3.333...
Math Tutor Explanation Using Fraction Pattern Method
For repeating decimals with a single repeating digit, you can quickly convert them to a fraction by placing the repeating digit over 9.
Step 1: Step 1: Recognize that the repeating decimal 0.3 is just one digit, 3, repeating endlessly
Step 2: Step 2: Place the repeating digit (3) over 9 to make the fraction 3/9
Step 1:
Step 2:
Math Tutor suggests: Master Repeating Decimals as Fractions
Explore more questions about expressing repeating and non-terminating decimals as fractions with these related problems.
FAQ on Repeating Decimals as Fractions
What does 0.3 repeating mean?
It means the digit 3 repeats endlessly after the decimal point, written as 0.333...
Are all repeating decimals rational numbers?
Yes, every repeating decimal can be written as a fraction, making it a rational number.
Can repeating decimals have more than one digit repeating?
Yes, examples include 0.1212... or 0.56 repeating.
Is 0.3 repeating the same as 1/3?
Yes, 0.3 repeating and 1/3 are exactly equal in value.
How do you convert longer repeating decimals to fractions?
Set a variable equal to the decimal, multiply to shift the repeat, subtract the equations, and solve for the variable.
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