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Brilliant_brown [7]

3 years ago

10

What is 3.659090909090909 as a fraction?

1 answer:

Radda [10]3 years ago

5 0

There is not much that can be done to figure out how to write 3.659090909090909 as a fraction, except to literally use what the decimal portion of your number, the <span>.659090909090909 </span>, means.

Since there are 16 digits in 659090909090909 , the very last digit is the "10000000000000000th" decimal place.

So we can just say that .659090909090909 is the same as 659090909090909 /10000000000000000.

<span>The fraction fmtterm: Can't handle [-2147483648/-2147483648] 3? is not reduced to lowest terms. We can reduce this fraction to lowest
terms by dividing both the numerator and denominator by -2.14748e+09.
</span>

<span>Why divide by -2.14748e+09? -2.14748e+09 is the Greatest Common Divisor (GCD)
or Greatest Common Factor (GCF) of the numbers 6.59091e+14 and 1e+16.
So, this fraction reduced to lowest terms is</span>

<span>So your final answer is: <span>3.659090909090909 </span>can be written as the fraction</span>

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A.

$x = \frac{7\sqrt{6}{3}$

$y = \frac{7\sqrt{6}}{3}$

Step-by-step explanation:

Reference angle = 60°

Opposite = $\frac{7\sqrt{2}}{2}$

Hypotenuse = x

Adjacent = y

✔️To find x, apply the trigonometric function SOH:

Sin 60° = Opp/Hyp

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$\frac{\sqrt{3}}{2} = \frac{\frac{7\sqrt{2}}{2}}{x}$ (sin 60 = √3/2)

$\frac{\sqrt{3}}{2} = \frac{7\sqrt{2}}{2}*\frac{1}{x}$

$\frac{\sqrt{3}}{2} = \frac{7\sqrt{2}}{2x}$

Cross multiply

$\sqrt{3}*2x = 7\sqrt{2}*2$

$2\sqrt{3}*x = 14\sqrt{2}$

Divide both sides by 2

$\sqrt{3}*x = 7\sqrt{2}$

Divide both sides by √3

$x = \frac{7\sqrt{2}}{\sqrt{3}}$

Rationalize

$x = \frac{7\sqrt{2}*\sqrt{3}}{\sqrt{3}*\sqrt{3}}$

$x = \frac{7\sqrt{6}{3}$

✔️To find y, apply the trigonometric function TOA:

Tan 60° = Opp/Adjacent

$Tan 60° = \frac{\frac{7\sqrt{2}}{2}}{y}$

$\sqrt{3} = \frac{\frac{7\sqrt{2}}{2}}{y}$ (tan 60 = √3)

$\sqrt{3} = \frac{7\sqrt{2}}{2}*\frac{1}{y}$

$\sqrt{3} = \frac{7\sqrt{2}}{2y}$

Cross multiply

$\sqrt{3}*2y = 7\sqrt{2}$

$2\sqrt{3}*y = 7\sqrt{2}$

Divide both sides by √3

$y = \frac{7\sqrt{2}}{\sqrt{3}}$

Rationalize

$y = \frac{7\sqrt{2}*\sqrt{3}}{\sqrt{3}*\sqrt{3}}$

$y = \frac{7\sqrt{6}}{3}$

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