Question

Convert 75 in.^3 to cubic decimeters. Round your answer to the nearest thousandth, if necessary.

a) 1.229 cubic decimeters
b) 0.750 cubic decimeters
c) 0.075 cubic decimeters
d) 122.856 cubic decimeters

Answer 1

To convert 75 cubic inches to cubic decimeters, multiply by (2.54³) and then divide by 1000. The result is 1.229 cubic decimeters, rounded to the nearest thousandth.

Step-by-step explanation:

To convert 75 in.³ to cubic decimeters, we first need to convert the volume from cubic inches to cubic centimeters and then to cubic decimeters. We know that one inch is equal to 2.54 centimeters, so to find the volume in cubic centimeters, we raise this conversion factor to the third power because we are dealing with cubic units:

(75 in.³) × (2.54 cm/in)³ = (75) × (2.54³) cm³

Once we have the volume in cubic centimeters, we then convert to cubic decimeters by knowing that one cubic decimeter is equal to 1000 cubic centimeters. Thus, we divide the volume in cubic centimeters by 1000 to get cubic decimeters:

(2.54³) × 75 cm³ / 1000 = 1.229 dm³

Therefore, 75 in.³ is equal to 1.229 cubic decimeters, rounded to the nearest thousandth.