Rational Numbers Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Express 0.36โ€พ0.\overline{36} as a fraction in simplest form.

Solution

  1. 1
    Let x=0.363636โ€ฆx = 0.363636\ldots Multiply both sides by 100: 100x=36.363636โ€ฆ100x = 36.363636\ldots
  2. 2
    Subtract the original: 100xโˆ’x=36100x - x = 36, so 99x=3699x = 36.
  3. 3
    Solve: x=3699=411x = \frac{36}{99} = \frac{4}{11}.

Answer

411\frac{4}{11}
A repeating decimal is always a rational number. Multiplying by a power of 10 that shifts the repeating block, then subtracting, eliminates the infinite repetition and yields a fraction.

About Rational Numbers

Numbers that can be expressed as a ratio of two integers (ab\frac{a}{b} where bโ‰ 0b \neq 0).

Learn more about Rational Numbers โ†’

More Rational Numbers Examples

Example 1 easy

Place the following numbers in order from least to greatest: [formula], [formula], [formula].

Example 3 easy

Which is greater: [formula] or [formula]?

Example 4 medium

Order these numbers from least to greatest: [formula], [formula], [formula].

โ† All Rational Numbers Examples Rational Numbers Concept