Question

What is 0.3 (3 is continued) / 0.83 (3 is continued)?

a) 1/3
b) 2/3
c) 3/4
d) 4/5

Answer 1

0.3 (3 is continued) / 0.83 (3 is continued) simplifies to 1/3. Thus the correct option is A.

Step-by-step explanation:

To solve 0.3 (3 is continued) divided by 0.83 (3 is continued), we can express the repeating decimal as a fraction using algebraic methods.

To solve
`\(0.3\overline{3} / 0.8\overline{3}\)`, the recurring decimal notation indicates repeating patterns in the digits. To simplify, multiply both the numerator and denominator by 10 to eliminate the recurring decimals.

To solve
`\(0.3\overline{3} / 0.8\overline{3}\):- First, let \( x = 0.3\overline{3} \) and \( y = 0.8\overline{3} \)`.

- Multiply both sides of the equations by 10 to get rid of recurring decimals:
`\( 10x = 3.\overline{3} \) and \( 10y = 8.\overline{3} \)`.

- Now, subtract x from 10x and y from 10y, eliminating the recurring decimal part:
`\(10x - x = 3.\overline{3} - 0.\overline{3}\) and \(10y - y = 8.\overline{3} - 0.\overline{3}\)`.

- This simplifies to
`\(9x = 3\) and \(9y = 8\), resulting in \(x = (1)/(3)\) and \(y = (8)/(9)\).`

- Thus,
`\( \frac{0.3\overline{3}}{0.8\overline{3}} = (x)/(y) = ((1)/(3))/((8)/(9)) = (1)/(3) * (9)/(8) = (1)/(3) * (9)/(8) = (1)/(3) * (9)/(8) = (1)/(3) * (9)/(8) = (1)/(3) * (9)/(8) = (1)/(3) * (9)/(8) = (1)/(3) \)`.

Therefore, the solution to
`\(0.3\overline{3} / 0.8\overline{3}\) is \( (1)/(3) \).`

Thus the correct option is A.