which of the following numbers would fall between $\frac{1}{3}$ and $\frac{2}{3}$ on a number line?

select all answers that apply.

a $2^{-3}$
b $\sqrt{2}$
c $0.48$
d $\frac{4}{7}$

Question

which of the following numbers would fall between $\frac{1}{3}$ and $\frac{2}{3}$ on a number line?

select all answers that apply.

a $2^{-3}$
b $\sqrt{2}$
c $0.48$
d $\frac{4}{7}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [], "new_concepts": [ "Real Number Comparison", "Fraction to Decimal Conversion", "Number Line Intervals" ], "current_concepts": [ "Real Number Comparison", "Fraction to Decimal Conversion", "Number Line Intervals" ] } ## Convert the interval boundaries to decimals $$ \begin{aligned} \frac{1}{3} &\approx 0.333... \ \frac{2}{3} &\approx 0.667... \ \text{Interval: } & (0.333, 0.667) \end{aligned} $$ ## Evaluate each option $$ \begin{aligned} \text{A: } 2^{-3} &= \frac{1}{8} = 0.125 otin (0.333, 0.667) \ \text{B: } \sqrt{2} &\approx 1.414 otin (0.333, 0.667) \ \text{C: } 0.48 &\in (0.333, 0.667) \ \text{D: } \frac{4}{7} &\approx 0.571 \in (0.333, 0.667) \end{aligned} $$ ## Determine the correct options $$ \text{Correct options: C and D} $$

(A) $2^{-3}$

(B) $\sqrt{2}$

(C) $0.48$

(D) $\frac{4}{7}$

{ "elements": [ { "type": "line", "params": [[-0.5, 0], [2.0, 0]], "properties": { "strokeColor": "#583C87", "strokeWidth": 2 } }, { "type": "point", "params": [[0.333, 0]], "properties": { "name": "1/3", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[0.667, 0]], "properties": { "name": "2/3", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[0.125, 0]], "properties": { "name": "A (0.125)", "size": 3, "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [[1.414, 0]], "properties": { "name": "B (1.41)", "size": 3, "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [[0.48, 0]], "properties": { "name": "C (0.48)", "size": 4, "color": "#55DDF2", "withLabel": true } }, { "type": "point", "params": [[0.571, 0]], "properties": { "name": "D (4/7)", "size": 4, "color": "#55DDF2", "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Real Number Comparison" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Convert the interval boundaries to decimals

Evaluate each option

Determine the correct options

Answer: