3 years ago

Solve the following

Mathematics

1 answer:

Anastaziya [24]3 years ago

3 0

Answer:

|a-b| = b-a when a<b

104159/33000

Step-by-step explanation:

If a<b then a-b will always be negative. To get the absolute value, we can take -(a-b) = -a+b = b-a.

Let x = 3.12789789789...

We isolate the repeating decimal to start after the decimal, so we multiply by 100.

100x = 312.789789789...

We want to multiply by 10 for each digit that repeats (in this case 3), to get the repeating part to the left of the decimal.

100000x = 312789.789789

Subtracting the two...

x(100000-100) = 312789.789789 - 312.789789

99900x = 312477

x = 312477/99000 = 104159/33000

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