Answer: W = 6.3
w ÷ 9 = 0.7
1. We need to convert the non-repeating decimal (0.7) into a rational number. We can rewrite the given number as a fraction, where the numerator is equal to the number after then decimal point, and the denominator is equal to [tex]10^n[/tex], when n is the number of decimal places. In the problem, n equals 1.
w ÷ 9 = [tex]\frac{7}{10}[/tex]
2. Now, we'll need to factor the integer, which is 9. To do that, repeatedly divide it by the ascending sequence of primes (2, 3, 5...). The number of times that each prime divides the original integer becomes its exponent in the final result. In the problem, 3 to the 2nd power is 9.
3 x 3 = 9
w ÷ 9 = [tex]\frac{7}{10}[/tex] ⇒ [tex]\frac{w}{3^2}=\frac{7}{2\times5}[/tex]
Hence, W = 63/10, but we aren't done. We'll need to divide 63 by 10.
63 ÷ 10 = 6.3
Our final answer is 6.3
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