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3 years ago

Express 1)32.12353535... 2)2.3333...+4.15151515... as a fraction in simplest form

1 answer:

6 0

(1) Suppose x = 32.12353535... . Then 100x = 3212.353535... and 10000x = 321235.353535... .

Subtracting these gives

10000x - 100x = 321235.353535... - 3212.353535...

9900x = 321235 - 3212

9900x = 318023

x = 318023/9900

(2) By the same process as above, we start with

x = 2.333...

y = 4.151515...

Then

10x = 23.333...

==> 10x - x = 23.333... - 2.333...

==> 9x = 23 - 2

==> x = 21/9

and

100y = 415.151515...

==> 100y - y = 415.151515... - 4.151515

==> 99y = 415 - 4

==> y = 411/99

After this, we get

x + y = 2.333... + 4.151515...

==> x + y = 21/9 + 411/99

==> x + y = 231/99 + 411/99

==> x + y = 642/99 = 214/33

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