How do you convert 0.23 (3 repeating) as a fraction?

Question

How do you convert 0.23 (3 repeating) as a fraction?

2 Answers

Impact of this question

94028 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-06T20:37:35

$\frac{7}{30}$ $7/30$

Explanation:

$0.23$ $0.23$ with $3$ $3$ repeating can be written as $0.2 . 3$ $0.2dot3$ , where the dot on top of the $3$ $3$ means a repeating number or pattern of numbers.

$x = 0.2 . 3$ $x = 0.2dot3$

$10 x = 2 . . 3$ $10x = 2.dot3$

$100 x = 23 . . 3$ $100x=23.dot3$

$90 x = 100 x - 10 x$ $90x = 100x - 10x$

$90 x = 23 . . 3 - 2 . . 3$ $90x = 23.dot3 - 2.dot3$

$90 x = 23 - 2 = 21$ $90x = 23 - 2 = 21$

$90 x = 21$ $90x = 21$

$x = \frac{21}{90}$ $x = 21/90$

$= \frac{7}{30}$ $= 7/30$

Answer 2 · 2018-03-06T20:38:46

See a solution process below:

Explanation:

First, we can write:

$x = 0.2 ¯ 3$ $x = 0.2bar3$

Next, we can multiply each side by $10$ $10$ giving:

$10 x = 2.3 ¯ 3$ $10x = 2.3bar3$

Then we can subtract each side of the first equation from each side of the second equation giving:

$10 x - x = 2.3 ¯ 3 - 0.2 ¯ 3$ $10x - x = 2.3bar3 - 0.2bar3$

We can now solve for $x$ $x$ as follows:

$10 x - 1 x = (2.3 + 0.0 ¯ 3) - (0.2 + 0.0 ¯ 3)$ $10x - 1x = (2.3 + 0.0bar3) - (0.2 + 0.0bar3)$

$(10 - 1) x = 2.3 + 0.0 ¯ 3 - 0.2 - 0.0 ¯ 3$ $(10 - 1)x = 2.3 + 0.0bar3 - 0.2 - 0.0bar3$

$9 x = (2.3 - 0.2) + (0.0 ¯ 3 - 0.0 ¯ 3)$ $9x = (2.3 - 0.2) + (0.0bar3 - 0.0bar3)$

$9 x = 2.1 + 0$ $9x = 2.1 + 0$

$9 x = 2.1$ $9x = 2.1$

$\frac{9 x}{9} = \frac{2.1}{9}$ $(9x)/color(red)(9) = 2.1/color(red)(9)$

$(color(red)(cancel(color(black)(9)))x)/cancel(color(red)(9)) = 10/10 xx 2.1/color(red)(9)$

$x = 21/90$

$x = (3 xx 7)/(3 xx 30)$

$x = (color(red)(cancel(color(black)(3))) xx 7)/(color(red)(cancel(color(black)(3))) xx 30)$

$x = 7/30$

Science

Math

Humanities

... and beyond

How do you convert 0.23 (3 repeating) as a fraction?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question