Convert a repeating–decimal mixed number to a fraction The intended value is 10.46(7) = 10.467777… (only the 7 repeats). Express this as a simplified fraction.

Introduction / Context:
This item converts a decimal with a non-repeating part followed by a single repeating digit into a fraction. The options indicate a denominator of 900, which matches a pattern where there are two non-repeating decimal digits and a repeating block of length one.

Given Data / Assumptions:

• Target number: 10.46(7) = 10.467777… (only the digit 7 repeats).
• Non-repeating part after decimal: “46” (two digits).
• Repeating block: “7” (one digit).
• Goal: obtain the simplest fraction.

Concept / Approach:
Separate the integer part and the fractional part with repetition. Let y = 0.46(7). For two non-repeating digits and one repeating digit, a standard shortcut is y = (467 − 46) / 900. Then add the integer part 10 to this fraction.

Step-by-Step Solution:
Let y = 0.46(7) = 0.467777…Compute numerator: 467 − 46 = 421.Denominator: since there are two non-repeating digits and one repeating, use 900 = 9 × 100.Thus y = 421/900.Add the integer part 10: 10 + 421/900 = (9000 + 421)/900 = 9421/900.

Verification / Alternative check:
Compute 9421 ÷ 900 ≈ 10.467777…, consistent with the intended decimal 10.46(7).

Why Other Options Are Wrong:
9422/900, 9435/900, and 9437/900 represent nearby values with slight numerator shifts; 8521/900 corresponds to 9.46(7), a different integer part, hence not matching the choices linked to this item.

Common Pitfalls:
Forgetting to subtract the non-repeating part from the combined block; using 990 instead of 900 when the non-repeating part has length two and the repeating block has length one.

Final Answer:
9421/900