Writing repeating decimals as fractions review

Review converting repeating decimals to fractions, and then try some practice problems.

Παρουσίαση δεκαδικού αριθμού σε μορφή κλάσματος

To convert a decimal to a fraction, we write the decimal number as a numerator, and we write its place value as the denominator.

Παράδειγμα 1: $0, 07$ ‍

Το

0, 07

ισοδυναμεί με

7

εκατοντάδες

. Έτσι, γράφουμε

7

στα

100

0, 07 = \frac{7}{100}

Let's look at an example.

Rewrite $0. \overset{―}{7}$ ‍ as a simplified fraction.

Let

x

equal the decimal:

$x = 0.7777 …$ ‍

Set up a second equation such that the digits after the decimal point are identical:

$\begin{aligned} 10 x & = 7.7777 … \\ x & = 0.7777 … \end{aligned}$ ‍

Subtract the two equations:

$9 x = 7$ ‍

Λύστε ως προς

x

$x = \frac{7}{9}$ ‍

Remember from the first step that

x

is equal to our repeating decimal, so:

$0. \overset{―}{7} = \frac{7}{9}$ ‍

Want to learn more about writing repeating decimals as fractions? Check out this video.

Πρόβλημα 1

Rewrite as a simplified fraction.

0. \overset{―}{2} = ?

Want to try more problems like this? Check out this exercise.

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