Select the decimal that is equivalent to (41)/(90)

Select the decimal that is equivalent to (41)/(90).

Choose 1 answer:

(A) 0.36 (B) 0.36 (C) 0.45 (D) 0.45 (E) None of the above

The correct answer and explanation is:

The correct answer is (E) None of the above.

Explanation:

To find the decimal equivalent of the fraction 4190\frac{41}{90}, we perform the division of 41 by 90.

First, divide 41 by 90: 41÷90=0.4555555…41 \div 90 = 0.4555555\ldots

This result is a repeating decimal. Specifically, the decimal is 0.45‾0.\overline{45}, which means the digits “45” repeat indefinitely.

Now, let’s break down the process:

1. When dividing 41 by 90, 90 does not fit into 41, so we add a decimal point and a zero to 41, making it 410.
2. 90 fits into 410 four times (because 90×4=36090 \times 4 = 360), so we subtract 360 from 410, which leaves a remainder of 50.
3. Bring down another zero, making it 500.
4. 90 fits into 500 five times (because 90×5=45090 \times 5 = 450), so we subtract 450 from 500, which leaves a remainder of 50 again.
5. The process continues, repeating the digits “45” indefinitely.

Thus, the decimal equivalent of 4190\frac{41}{90} is 0.4444…, or more precisely, 0.\overline{45}.

Since none of the given options (A), (B), (C), or (D) represent the correct repeating decimal, the correct answer is (E) None of the above.