convert 10.25mm to the nearest inch drill size?

a $\frac{23}{64}$

b $\frac{27}{64}$

c $\frac{13}{32}$

d $\frac{11}{32}$

Question

convert 10.25mm to the nearest inch drill size?

a $\frac{23}{64}$

b $\frac{27}{64}$

c $\frac{13}{32}$

d $\frac{11}{32}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Unit Conversion", "Inches to Millimeters" ], "new_concepts": [], "current_concepts": [ "Unit Conversion", "Inches to Millimeters", "Fractional Inch Conversion" ] } ## Convert millimeters to decimal inches $$ 10.25 \text{ mm} \div 25.4 \text{ mm/inch} \approx 0.40354 \text{ inches} $$ ## Convert decimal inches to fractional inches with a denominator of 64 $$ 0.40354 \times 64 = 25.82656 \approx 26 $$ $$ \frac{26}{64} \text{ inches} = \frac{13}{32} \text{ inches} $$ ## Compare fractional values to find the closest match $$ \begin{aligned} \text{Option A: } \frac{23}{64} &\approx 0.3594 \text{ inches} \ \text{Option B: } \frac{27}{64} &\approx 0.4219 \text{ inches} \ \text{Option C: } \frac{13}{32} = \frac{26}{64} &\approx 0.4063 \text{ inches} \ \text{Option D: } \frac{11}{32} = \frac{22}{64} &\approx 0.3438 \text{ inches} \end{aligned} $$ $$ |0.40354 - 0.40625| = 0.00271 \text{ (smallest difference)} $$

(A) $\frac{23}{64}''$

(B) $\frac{27}{64}''$

(C) $\frac{13}{32}''$

(D) $\frac{11}{32}''$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Unit Conversion" ] }

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QUESTION IMAGE

Question

Explanation:

Convert millimeters to decimal inches

Convert decimal inches to fractional inches with a denominator of 64

Compare fractional values to find the closest match

Answer: