Math / Numbers & Operations

QuestionA stack of 500 pieces of paper is 1.875 inches tall.
PART A Diego guesses that each piece of paper is 0.015 inches thick. Explain why Diego's answer is incorrect. Hint: Use the $f_{x}$ button to type out math expressions, fractions, and symbols more easily

Studdy Solution

STEP 1

1. A stack of 500 pieces of paper is 1.875 inches tall.
2. Diego guesses that each piece of paper is 0.015 inches thick.
3. We need to determine the actual thickness of each piece of paper and compare it to Diego's guess.

STEP 2

1. Calculate the actual thickness of one piece of paper.
2. Compare the calculated thickness to Diego's guess.

STEP 3

Calculate the actual thickness of one piece of paper by dividing the total height of the stack by the number of pieces of paper.
$\text{Actual thickness} = \frac{\text{Total height of stack}}{\text{Number of pieces of paper}}$
$\text{Actual thickness} = \frac{1.875 \text{ inches}}{500}$

STEP 4

Perform the division to find the actual thickness.
$\text{Actual thickness} = \frac{1.875}{500} = 0.00375 \text{ inches}$

STEP 5

Compare the actual thickness to Diego's guess of 0.015 inches.
- Diego's guess: $0.015 \text{ inches}$ - Actual thickness: $0.00375 \text{ inches}$
Since $0.00375 \text{ inches} < 0.015 \text{ inches}$ , Diego's guess is incorrect because he overestimated the thickness of each piece of paper.
The actual thickness of each piece of paper is $0.00375$ inches, which is significantly less than Diego's guess of $0.015$ inches.

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