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balu736 [363]
2 years ago
15

Write the recurring decimal 0.473737373... as a fraction.​

Mathematics
1 answer:
Semenov [28]2 years ago
4 0

Answer:

\frac{469}{990}

Step-by-step explanation:

We require 2 equations with the repeating digits after the decimal point.

By subtracting the 2 equations eliminates the repeating digits.

let x = 0.47373737.....

Multiply both sides by 100 and 10000, that is

100x = 47.3737... → (1)

10000x = 4737.3737.... → (2)

Subtract (1) from (2)

9900x = 4690 ( divide both sides by 9900 )

x = \frac{4690}{9900} = \frac{460}{990} ← in simplest form

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We know that angle MKJ is comprised of angle MKL and angle LKJ. That means if we add MKL and LKJ, we should get 80 degrees, which is the measure of angle MKJ.

MKL + LKJ= MKJ \implies \\ 2x+10+3x-5=80 \implies \\ 5x+5=80 \implies\\ 5x=75 \implies \\ x=15

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MKL=2(15)+10 = 40\\ LKJ=3*15-5=40

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