Question

find the decimal value of the postfix (rpn) expression. round answers to one decimal place (e.g. for an answer of 13.45 you would enter 13.5): 5 3 6 6 7 3 / - *

Answer 1

The decimal value of the postfix expression 5 3 6 6 7 3 / - * is 110.0 after evaluating the operations in the RPN sequence and rounding the final result to one decimal place.

Step-by-step explanation:

The given postfix (RPN) expression is 5 3 6 6 7 3 / - *.

To find the decimal value, we perform the operations in the order they appear, using a stack to hold operands until they are needed.

Here's the step-by-step evaluation:

1. Push 5 onto the stack.
2. Push 3 onto the stack.
3. Push 6 onto the stack.
4. Push 6 onto the stack.
5. Push 7 onto the stack.
6. Push 3 onto the stack.
7. Perform division: Pop 3 and 7 from the stack (7 / 3) and push the result, 2.3333333, onto the stack.
8. Perform subtraction: Pop 2.3333333 and 6 from the stack (6 - 2.3333333) and push the result, 3.6666667, onto the stack.
9. Perform multiplication: Pop 3.6666667 and 6 from the stack (6 * 3.6666667) and push the result onto the stack.
10. Perform multiplication: Pop the last two results (5 * the previous result), which gives us the final answer.

Using a calculator, step 9 gives us 22.0000002, and then multiplying by 5 (step 10) gives us 110.000001.

According to the rule of rounding to one decimal place, the final result is rounded to 110.0.