Reviewed by Yaren Fadiloglulari
What is 0.6 repeating as a Fraction?
Answer: 0.6 repeating as a fraction is 2/3
The decimal 0.6 repeating, often written as 0.666... with an infinite sequence of sixes, is a common recurring decimal in mathematics. Transforming repeating decimals to fractions helps us represent them precisely without an infinite sequence. Let's explore how 0.6 repeating can be written as a fraction.
Methods
Math Tutor Explanation Using Algebraic Method
This method uses an algebraic trick to convert a repeating decimal to a fraction by creating and solving an equation.
Step 1: Step 1: Let x equal 0.666...
Step 2: Step 2: Multiply both sides by 10 to move the decimal (10x = 6.666...)
Math Tutor Explanation Using Place Value Understanding
We recognize that each decimal place in 0.666... represents a fraction in powers of 10, and their infinite sum forms a geometric series.
Step 1: Step 1: Recognize 0.6 repeating as 0.6 + 0.06 + 0.006 + ...
Step 2: Step 2: Apply the geometric series sum formula with first term a = 0.6 and ratio r = 0.1
Step 1:
Step 2:
Math Tutor suggests: More Practice with Repeating Decimals and Fractions
Deepen your understanding of converting repeating decimals to fractions and explore more fraction-decimal conversions with these related questions.
FAQ on Repeating Decimals and Fractions
What does 0.6 repeating mean?
It means the digit 6 repeats indefinitely after the decimal point, so the decimal never ends.
Is 0.666... exactly equal to 2/3?
Yes, 0.666... and 2/3 represent the same value.
How do you write other repeating decimals as fractions?
Create an equation where x equals the decimal, multiply to shift the edge of the repeating part, subtract, then solve for x.
Can all repeating decimals be written as fractions?
Yes, all repeating (and terminating) decimals can be expressed as fractions with integer numerators and denominators.
Why do repeating decimals convert to simple fractions?
Repeating decimals are another form of rational numbers, which by definition can be expressed as fractions.
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