Solve the problem.
Find a conversion factor between cubicle inches and cubic yards. Write it in three forms
To find the conversion factor between cubic inches and cubic yards, we need to know the relationship between these two units.
1 cubic yard is equal to 46,656 cubic inches.
Therefore, the conversion factor can be written as:
1 cubic yard/46,656 cubic inches
or
1 cubic inch/46,656 cubic yards
or
46,656 cubic inches/1 cubic yard
To find a conversion factor between cubic inches and cubic yards, we need to determine the relationship between the two units. Let's break it down step-by-step:
Step 1: Determine the relationship between cubic inches and cubic yards.
1 cubic yard is equal to 36 inches in each dimension (length, width, and height). Therefore, to convert from cubic inches to cubic yards, we need to divide the number of cubic inches by 36^3 (since there are 36 inches in a yard, and we are dealing with three dimensions).
Step 2: Calculate the conversion factor.
The conversion factor can be calculated using the equation:
1 cubic yard = (1/36^3) cubic inches
Step 3: Simplify the conversion factor.
To simplify the conversion factor, we can evaluate (1/36)^3.
Calculating (1/36)^3:
(1/36)^3 = 1/(36*36*36)
= 1/46,656
So, the conversion factor between cubic inches and cubic yards is 1/46,656.
Writing the conversion factor in different forms:
1. Fraction form: 1/46,656
2. Decimal form: 0.000021433
Thus, the conversion factor between cubic inches and cubic yards can be written as 1/46,656 or approximately 0.000021433.
To find the conversion factor between cubic inches and cubic yards, we need to understand the relationship between the two units.
1. First, let's establish the conversion factor between cubic inches and cubic feet, as both cubic inches and cubic yards are commonly expressed in terms of cubic feet.
1 cubic foot (ft³) is equal to 12 inches (in) × 12 inches (in) × 12 inches (in), which is equal to 1,728 cubic inches (in³).
2. Next, we need to determine the conversion factor between cubic feet and cubic yards.
1 cubic yard (yd³) is equal to 3 feet (ft) × 3 feet (ft) × 3 feet (ft), which is equal to 27 cubic feet (ft³).
Now, let's combine these two conversion factors to find the conversion factor between cubic inches and cubic yards.
Conversion Factor:
1 cubic yard (yd³) = 27 cubic feet (ft³)
1 cubic foot (ft³) = 1,728 cubic inches (in³)
Multiply these two conversion factors together:
1 cubic yard (yd³) = 27 cubic feet (ft³) = 27 × 1,728 cubic inches (in³)
Simplifying the equation:
1 cubic yard (yd³) = 46,656 cubic inches (in³)
Therefore, the conversion factor between cubic inches and cubic yards is:
1 cubic yard (yd³) = 46,656 cubic inches (in³)
In three forms:
1. Fractional Form: 1 yd³ / 46,656 in³ (read as "1 cubic yard divided by 46,656 cubic inches")
2. Decimal Form: 0.0000214334705 yd³/in³
3. Exponential Form: 1.143 × 10^⁻⁵ yd³/in³ (read as "1.143 times 10 raised to the power of negative 5 cubic yards per cubic inch")