a jet flies at a rate of $1.3 \times 10^6$ feet per hour. written in scientific notation, which is the best estimate of how many feet the jet will travel in $2.8 \times 10^3$ hours?

$3 \times 10^3$ feet
$3 \times 10^6$ feet
$3 \times 10^9$ feet
$3 \times 10^{10}$ feet

Question

a jet flies at a rate of $1.3 \times 10^6$ feet per hour. written in scientific notation, which is the best estimate of how many feet the jet will travel in $2.8 \times 10^3$ hours?

$3 \times 10^3$ feet
$3 \times 10^6$ feet
$3 \times 10^9$ feet
$3 \times 10^{10}$ feet

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Scientific Notation" ], "new_concepts": [ "Scientific Notation Estimation" ], "current_concepts": [ "Scientific Notation", "Scientific Notation Estimation" ] } ## Set up the multiplication for total distance $$ \text{Distance} = \text{Rate} \times \text{Time} = (1.3 \times 10^6) \times (2.8 \times 10^3) $$ ## Estimate by rounding the coefficients $$ \begin{aligned} 1.3 &\approx 1 \ 2.8 &\approx 3 \ \text{Estimated Distance} &\approx (1 \times 3) \times (10^6 \times 10^3) \end{aligned} $$ ## Simplify the expression using exponent rules $$ \begin{aligned} 1 \times 3 &= 3 \ 10^6 \times 10^3 &= 10^{6+3} = 10^9 \ \text{Estimated Distance} &\approx 3 \times 10^9 \text{ feet} \end{aligned} $$

(A) $3 \times 10^3$ feet

(B) $3 \times 10^6$ feet (C) $3 \times 10^9$ feet

(D) $3 \times 10^{10}$ feet

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Scientific Notation" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set up the multiplication for total distance

Estimate by rounding the coefficients

Simplify the expression using exponent rules

Answer: