a penny, the 1-cent coin in u.s. currency, measures $1.55 \times 10^{-3}$ meters. how tall would a 1-dollar stack of pennies be?

give your answer as a number/word combination using the most reasonable metric prefix.

Question

a penny, the 1-cent coin in u.s. currency, measures $1.55 \times 10^{-3}$ meters. how tall would a 1-dollar stack of pennies be?

give your answer as a number/word combination using the most reasonable metric prefix.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Scientific Notation", "Metric Prefixes" ], "new_concepts": [], "current_concepts": [ "Scientific Notation", "Metric Prefixes", "Unit Conversion" ] } ## Calculate the number of pennies in a 1-dollar stack Using the *Scientific Notation* knowledge point $$ \begin{aligned} &\text{Value of 1 penny} = \$0.01\ &\text{Target value} = \$1.00\ &N = \frac{1.00}{0.01} = 100 = 10^2 \end{aligned} $$ ## Calculate the total height in meters Using the *Scientific Notation* knowledge point $$ \begin{aligned} &h_{\text{penny}} = 1.55 \times 10^{-3}\text{ m}\ &H = N \times h_{\text{penny}} = 10^2 \times (1.55 \times 10^{-3}\text{ m}) = 1.55 \times 10^{-1}\text{ m} = 0.155\text{ m} \end{aligned} $$ ## Convert to a reasonable metric prefix Using the *Metric Prefixes* knowledge point $$ \begin{aligned} &0.155\text{ m} = 15.5\text{ cm} = 155\text{ mm}\ &\text{Most reasonable prefix: centimeters} \end{aligned} $$ A penny, the 1-cent coin in U.S. Currency, measures $1.55 \times 10^{-3}$ meters. How tall would a 1-dollar stack of pennies be? Give your answer as a number/word combination using the most reasonable metric prefix. 15.5 centimeters { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Scientific Notation" ] }

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Question

Explanation:

Calculate the number of pennies in a 1-dollar stack

Calculate the total height in meters

Convert to a reasonable metric prefix

Answer: