Just A Decimal!

Algebra Level 1

Even though the digits of the decimal 10.5555555555 … \Large \color{#3D99F6}{10.5555555555}\ldots repeat forever, it can be written a simple fraction! Which of these fractions is equivalent to this decimal number?

90 7 \frac{90}{7} 89 6 \frac{89}{6} 95 9 \frac{95}{9} 60 78 \frac{60}{78}

View wiki
Ankan Biswas by Ankan Biswas , 20, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

7 solutions

Joshua Ong
Nov 3, 2014

Let 10. 5 ‾ 10.\overline{5} be x . x. 10 x = 105. 5 ‾ 10x=105.\overline{5} 9 x = 10 x − x = 105. 5 ‾ − 10. 5 ‾ = 95 9x=10x-x=105.\overline{5}-10.\overline{5}=95 x = 95 9 x=\boxed{\frac{95}{9}}

9 Helpful 0 Interesting 0 Brilliant 0 Confused
Sunil Pradhan
Oct 27, 2014

Let 10.5555... = x then 10x = 105.555...

10x – x = 105.5555... – 10.5555... = 95/9

2 Helpful 0 Interesting 0 Brilliant 0 Confused

10x – x = 105.5555... – 10.5555.. 9x = 95 x = 95/9

Ritu Roy - 6 years, 7 months ago
Caeo Tan
Sep 6, 2015

I discovered this, 0.nnnn.......=n/9 (0<n<9)

So 10.55555.... can be expressed as 10+5/9=95/9

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Farshid Vahedian
Apr 28, 2015

10X=95+X 10X=105.55555=95+10.55555 which is equal to X

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Tang Changyang
Nov 22, 2014

10.555555.... = 10 + 0.555555...

We can see the 0.555555... part as a sum of geometric progression, which the first term(a)is 0.5 and common ratio (r) is 0.1.

Using the formula of sum to infinity which is a/(1-r), we will get that 0.555555.. is 5/9

10.555555... =10 +0.555555..... =10 +5/9 =95/9

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Kabir Bagai
Nov 16, 2014

Decimal for 1/9 is 1.11111111111111111.....

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Soummo Paul
Oct 26, 2014

10.555.... = 10 + .555.... Let, .555..... = a; then, 10 a = 5.555... = 5 + .555.... = 5 + a So, 9a = 5 so a = 5/9. Now, 10.555... = 10 + 5/9 = 95/9

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...