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Write each repeating decimal as a fraction in the simplest form.

0.4¯

Short Answer

Expert verified

The simplest form is =49.

Step by step solution

01

Step 1. Interpret the notation.

0.4¯means 0.4444…..

02

Step 2. Assign a variable.

Let N = 0.4444…...

03

Step 3. Decide by what to multiply.

Since only one-digit repeats so we multiply each side by 10.

10N = 10(0.4444…..)

10N = 4.4444…..

04

Step 4. Solve for N.

Subtract N from 10N, so that the repeating part eliminates.

10N=4.4444.-N=0.4444.9N=4

Then divide each side by 9 and simplify.

9N9=49

N=49

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