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Mars2501 [29]
3 years ago
11

Prove algebraically that the recurring decimal 0.472 can be written as 17 36

Mathematics
1 answer:
Katen [24]3 years ago
8 0

Given:

The recurring decimal is 0.47\overline{2}.

To prove:

Algebraically that the recurring decimal 0.47\overline{2} can be written as \dfrac{17}{36}.

Proof:

Let,

x=0.47\overline{2}

x=0.472222...

Multiply both sides by 100.

100x=47.2222...     ...(i)

Multiply both sides by 10.

1000x=472.2222...        ...(ii)

Subtract (i) from (ii).

1000x-100x=472.2222...-47.2222...

900x=425

Divide both sides by 900.

x=\dfrac{425}{900}

x=\dfrac{17}{36}

So, 0.47\overline{2}=\dfrac{17}{36}.

Hence proved.

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5 0
3 years ago
Each of the walls in Harvey’s shed are square and have an area of 84 square feet. What is the approximate height, to the nearest
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Answer:

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6 0
3 years ago
Tamara is at the store buying pencils. There is a package with 4 pencils that costs $6 or a package with 5 pencils that costs $7
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8 0
1 year ago
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Answer:

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hope this helps! :)

6 0
2 years ago
Read 2 more answers
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