How to write 1.4444… (4 repeating) as a fraction?

Expert answers to "How to write 1.4444… (4 repeating) as a..."

mascaraspx2

2023-01-08

How to write

1.4444 \dots

(4 repeating) as a fraction?

bagosiwp2

Beginner2023-01-09Added 16 answers

Extra close brace or missing open brace

10 x = 1.44444444444444444444 \dots . - - - (2)

(2) - (1)

9 x = 1.3

The repeated numbers are all false.

x = \frac{1.3}{9} = \frac{13}{90}

osloturvpn

Beginner2023-01-10Added 1 answers

It should be noted that repeating decimal places can be identified by placing a viniculum (bar) over the repeated digits.
So we can write

0.1 \overset{―}{4}

to signify

0.14444 \dots

Note that

0 . \overset{―}{9} = 1

. Therefore

\frac{4}{9} = 0 . \overset{―}{4}

So:

0.1 \overset{―}{4} = 0.4 \overset{―}{4} - 0.3 = \frac{4}{9} - \frac{3}{10} = \frac{40}{90} - \frac{27}{90} = \frac{13}{90}

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