What is 3.51 repeated as a mixed number?

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Answer 1 · 2018-02-19T11:43:27

See a solution below: Assuming 3.51515151...

First, we can write:

#x = 3.bar51#

Next, we can multiply each side by #100# giving:

#100x = 351.bar51#

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

#100x - x = 351.bar51 - 3.bar51#

We can now solve for #x# as follows:

#100x - 1x = (351 + 0.bar51) - (3 + 0.bar51)#

#(100 - 1)x = 351 + 0.bar51 - 3 - 0.bar51#

#99x = (351 - 3) + (0.bar51 - 0.bar51)#

#99x = 348 + 0#

#99x = 348#

#(99x)/color(red)(99) = 348/color(red)(99)#

#(color(red)(cancel(color(black)(99)))x)/cancel(color(red)(99)) = (3 xx 116)/color(red)(3 xx 33)#

#x = (color(red)(cancel(color(black)(3))) xx 116)/color(red)(color(black)(cancel(color(red)(3))) xx 33)#

#x = 116/33#

We can now convert this to a mixed number:

#116/33 = (99 + 17)/33 = 99/33 + 17/33 = 3 + 17/33 = 3 17/33#

This same process can be used if you are looking for 3.5111111...

Instead of multiplying by 100 multiply by 10 because there is only one number repeating.