When 4.036 is divided by 0.04, what is the resulting quotient?

Introduction / Context:
This question focuses on division of decimals and the effect of moving decimal points in both the dividend and divisor. It is a basic but important skill for handling decimal operations without always relying on a calculator and appears frequently in decimal fraction sections of aptitude exams.

Given Data / Assumptions:

• Dividend (number being divided) = 4.036.
• Divisor (number we divide by) = 0.04.
• We are asked to compute the quotient 4.036 ÷ 0.04.
• All values are exact decimals, and no rounding is requested.

Concept / Approach:
To divide by a decimal, a standard approach is to convert the divisor into a whole number by multiplying both the dividend and divisor by the same power of 10. This keeps the value of the quotient unchanged but allows us to perform a simpler division by a whole number. Specifically, if the divisor has two digits after the decimal, we multiply both numbers by 100 to remove the decimal from the divisor.

Step-by-Step Solution:
We need to evaluate 4.036 ÷ 0.04.The divisor 0.04 has two decimal places. Multiply both numbers by 100.4.036 × 100 = 403.6.0.04 × 100 = 4.Now compute the simpler quotient: 403.6 ÷ 4.Perform the division: 4 goes into 40 ten times, leaving 0; bring down 3 to get 3.0, which gives 0 with remainder 3. Bring down 6 to get 36, which gives 9.Thus 403.6 ÷ 4 = 100.9.Therefore, 4.036 ÷ 0.04 = 100.9.

Verification / Alternative check:
We can check the result by reversing the operation. Multiply the quotient by the divisor: 100.9 × 0.04. First, 100.9 × 4 = 403.6. Then move the decimal two places left to account for dividing by 100, giving 4.036. This matches the original dividend exactly, so our quotient 100.9 is confirmed as correct.

Why Other Options Are Wrong:
Option 1.009 would correspond to dividing 4.036 by 4, not by 0.04. Option 10.09 is off by a factor of 10 and results from shifting the decimal incorrectly only once. Option 1009 is a factor of 10 larger than the correct answer and would imply an incorrect scaling. Option 0.1009 is far too small and does not reflect division by a number less than 1, which should increase the result, not decrease it.

Common Pitfalls:
Common errors include moving the decimal point in only the divisor but not the dividend, or shifting the decimal in opposite directions. Another frequent mistake is forgetting that dividing by a small decimal (less than 1) should produce a larger quotient. Keeping track of how many decimal places you shift and always adjusting both numbers by the same power of 10 help to avoid these mistakes.

Final Answer:
The quotient when 4.036 is divided by 0.04 is 100.9.