the radii of the planets in the solar system are given. arrange the planets in increasing order by the lengths of their radii.

saturn: $5.82 \times 10^4$ kilometers
mercury: $2.44 \times 10^3$ kilometers
earth: $6.37 \times 10^3$ kilometers
uranus: $2.54 \times 10^4$ kilometers
neptune: $2.46 \times 10^4$ kilometers
mars: $3.39 \times 10^3$ kilometers
venus: $6.05 \times 10^3$ kilometers
jupiter: $6.99 \times 10^4$ kilometers

Question

the radii of the planets in the solar system are given. arrange the planets in increasing order by the lengths of their radii.

saturn: $5.82 \times 10^4$ kilometers
mercury: $2.44 \times 10^3$ kilometers
earth: $6.37 \times 10^3$ kilometers
uranus: $2.54 \times 10^4$ kilometers
neptune: $2.46 \times 10^4$ kilometers
mars: $3.39 \times 10^3$ kilometers
venus: $6.05 \times 10^3$ kilometers
jupiter: $6.99 \times 10^4$ kilometers

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Comparing Scientific Notation" ], "new_concepts": [], "current_concepts": [ "Scientific Notation", "Comparing Scientific Notation" ] } ## Group values by powers of ten Using the *Comparing Scientific Notation* knowledge point $$ \begin{aligned} &\text{Group 1 } (10^3\text{ km}): \ &\quad \text{Mercury: } 2.44 \times 10^3 \ &\quad \text{Mars: } 3.39 \times 10^3 \ &\quad \text{Venus: } 6.05 \times 10^3 \ &\quad \text{Earth: } 6.37 \times 10^3 \ &\text{Group 2 } (10^4\text{ km}): \ &\quad \text{Neptune: } 2.46 \times 10^4 \ &\quad \text{Uranus: } 2.54 \times 10^4 \ &\quad \text{Saturn: } 5.82 \times 10^4 \ &\quad \text{Jupiter: } 6.99 \times 10^4 \end{aligned} $$ ## Compare coefficients within each group Using the *Comparing Scientific Notation* knowledge point $$ \begin{aligned} &2.44 < 3.39 < 6.05 < 6.37 \ &\text{Mercury} < \text{Mars} < \text{Venus} < \text{Earth} \ \ &2.46 < 2.54 < 5.82 < 6.99 \ &\text{Neptune} < \text{Uranus} < \text{Saturn} < \text{Jupiter} \end{aligned} $$ ## Combine groups for final increasing order Using the *Comparing Scientific Notation* knowledge point $$ \begin{aligned} &\text{Mercury} < \text{Mars} < \text{Venus} < \text{Earth} < \text{Neptune} < \text{Uranus} < \text{Saturn} < \text{Jupiter} \end{aligned} $$ The planets arranged in increasing order by the lengths of their radii are: 1. Mercury ($2.44 \times 10^3$ kilometers) 2. Mars ($3.39 \times 10^3$ kilometers) 3. Venus ($6.05 \times 10^3$ kilometers) 4. Earth ($6.37 \times 10^3$ kilometers) 5. Neptune ($2.46 \times 10^4$ kilometers) 6. Uranus ($2.54 \times 10^4$ kilometers) 7. Saturn ($5.82 \times 10^4$ kilometers) 8. Jupiter ($6.99 \times 10^4$ kilometers) { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Comparing Scientific Notation" ] }

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Question

Explanation:

Group values by powers of ten

Compare coefficients within each group

Combine groups for final increasing order

Answer: