Converting Repeating Decimals to Fractions
Converting repeating decimals to fractions is a Grade 6 rational numbers skill in Big Ideas Math Advanced 1, Chapter 12: Rational Numbers. Students use algebraic reasoning — setting the decimal equal to a variable, multiplying to shift the repeating block, then subtracting to eliminate the repeating part — to express repeating decimals as exact fractions.
Key Concepts
To convert a repeating decimal to a fraction: Let $x$ equal the repeating decimal, multiply $x$ by the appropriate power of 10 to shift the decimal point so the repeating block aligns, subtract the original equation, then solve for $x$.
Common Questions
How do you convert a repeating decimal to a fraction?
Let x equal the repeating decimal. Multiply both sides by 10 (or 100 for two-digit repeats) to shift the repeating block. Subtract the original equation, then solve for x. For example, 0.333... = 1/3.
What is a repeating decimal?
A repeating decimal is a decimal in which one or more digits repeat infinitely. Examples include 0.333... (one-third), 0.666... (two-thirds), and 0.142857142857... (one-seventh).
Why is every repeating decimal a rational number?
A rational number can be expressed as a fraction of two integers. Since every repeating decimal can be converted to a fraction using algebra, all repeating decimals are rational numbers.
Where is this skill taught in Big Ideas Math Advanced 1?
Converting repeating decimals to fractions is covered in Chapter 12: Rational Numbers of Big Ideas Math Advanced 1, the Grade 6 math textbook.