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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, comma, 07
Το 0, comma, 0, start color #11accd, 7, end color #11accd ισοδυναμεί με start color #11accd, 7, end color #11accd start text, start color #1fab54, ε, κ, α, τ, ο, ν, τ, α, with, \', on top, δ, ε, ς, end color #1fab54, end text. Έτσι, γράφουμε start color #11accd, 7, end color #11accd στα start color #1fab54, 100, end color #1fab54.
0, comma, 07, equals, start fraction, start color #11accd, 7, end color #11accd, divided by, start color #1fab54, 100, end color #1fab54, end fraction

But what about repeating decimals?

Let's look at an example.
Rewrite 0, point, start overline, 7, end overline as a simplified fraction.
Let x equal the decimal:
x, equals, 0, point, 7777, point, point, point
Set up a second equation such that the digits after the decimal point are identical:
10x=7.7777...x=0.7777...\large{\begin{aligned} 10x &= 7.7777...\\ x &= 0.7777... \end{aligned}}
Subtract the two equations:
9, x, equals, 7
Solve for x:
x, equals, start fraction, 7, divided by, 9, end fraction
Remember from the first step that x is equal to our repeating decimal, so:
0, point, start overline, 7, end overline, equals, start fraction, 7, divided by, 9, end fraction
Want to learn more about writing repeating decimals as fractions? Check out this video.

Practice

Πρόβλημα 1
Rewrite as a simplified fraction.
0, point, start overline, 2, end overline, equals, question mark
  • Η απάντησή σου έπρεπε να είναι
  • ένα γνήσιο κλάσμα, όπως το 1, slash, 2 ή το 6, slash, 10
  • ένα καταχρηστικό κλάσμα, όπως το 10, slash, 7 ή το 14, slash, 8
  • ένας μεικτός αριθμός, όπως το 1, space, 3, slash, 4

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