A decimal number 47.2506 is expressed in terms of place value units as 47.2506 = 4*A + 7*B + 2*C + 5*D + 6*E, where A, B, C, D and E represent the standard place value units 10, 1, 0.1, 0.01 and 0.0001 respectively. What is the value of 5*A + 3*B + 6*C + D + 3*E?

Introduction / Context:
This question assesses your understanding of decimal place values and how a decimal number can be decomposed into a linear combination of place value units. By carefully matching the digits of the decimal 47.2506 with their corresponding place values, you can identify the numerical values of A, B, C, D and E. You then substitute these into another linear expression to find its value.

Given Data / Assumptions:

• Number given: 47.2506.
• Representation: 47.2506 = 4*A + 7*B + 2*C + 5*D + 6*E.
• A, B, C, D and E represent standard decimal place value units.
• We are told that A = 10, B = 1, C = 0.1, D = 0.01, E = 0.0001.
• We must compute the value of 5*A + 3*B + 6*C + D + 3*E.

Concept / Approach:
The number 47.2506 has digits in the tens, ones, tenths, hundredths and ten-thousandths places. Therefore, 4 is in the tens place, 7 is in the ones place, 2 is in the tenths place, 5 is in the hundredths place, and 6 is in the ten-thousandths place. These correspond exactly to multiplying 4, 7, 2, 5 and 6 by 10, 1, 0.1, 0.01 and 0.0001 respectively. After confirming this mapping, we plug the same values of A, B, C, D and E into the new expression and evaluate.

Step-by-Step Solution:
Step 1: Confirm the mapping: A = 10, B = 1, C = 0.1, D = 0.01, E = 0.0001. Step 2: Check the given decomposition: 4*A = 4 * 10 = 40. Step 3: 7*B = 7 * 1 = 7, so 40 + 7 = 47. Step 4: 2*C = 2 * 0.1 = 0.2, bringing the total to 47.2. Step 5: 5*D = 5 * 0.01 = 0.05, making the running total 47.25. Step 6: 6*E = 6 * 0.0001 = 0.0006, giving 47.2506, which matches the original decimal. Step 7: Now evaluate 5*A + 3*B + 6*C + D + 3*E: 5*A = 5 * 10 = 50. Step 8: 3*B = 3 * 1 = 3, so subtotal is 50 + 3 = 53. Step 9: 6*C = 6 * 0.1 = 0.6, subtotal is 53.6. Step 10: D = 0.01, so subtotal becomes 53.61. Step 11: 3*E = 3 * 0.0001 = 0.0003, final result is 53.6103.
Verification / Alternative check:
You can quickly check whether any other interpretation of A, B, C, D, E would still satisfy the original equality 47.2506 = 4*A + 7*B + 2*C + 5*D + 6*E. Using the standard place values is the most natural and consistent interpretation and recreates the number exactly.
Why Other Options Are Wrong:
55.6003, 53.603 and 153.6003 do not equal 5*A + 3*B + 6*C + D + 3*E when A, B, C, D and E are the standard decimal place values.
Common Pitfalls:
Learners may confuse which digit corresponds to which place value or may miscalculate small decimal contributions such as E = 0.0001. Rounding intermediate calculations too aggressively can also lead to slight but significant errors in the final result.
Final Answer:
The value of the expression 5*A + 3*B + 6*C + D + 3*E is 53.6103.