Carry out the following conversions: (d) 1.955 m³ to yd³

Verified step by step guidance

1. Identify the conversion factors needed: 1 meter (m) = 1.09361 yards (yd). Therefore, 1 cubic meter (m^3) = (1.09361 yd)^3.
2. Calculate the conversion factor for cubic meters to cubic yards: (1.09361 yd)^3 = 1.09361^3 yd^3.
3. Multiply the given volume in cubic meters by the conversion factor to convert to cubic yards: 1.955 m^3 * (1.09361^3 yd^3/m^3).
4. Simplify the expression to find the volume in cubic yards.
5. Ensure the units are correctly converted and the final answer is expressed in yd^3.

Key Concepts

Volume Units

Volume is a measure of the three-dimensional space an object occupies, commonly expressed in units such as cubic meters (m³) and cubic yards (yd³). Understanding these units is essential for converting between different volume measurements, as they represent different scales of volume.

Unit Conversion

Unit conversion involves changing a quantity expressed in one unit to another unit without changing its value. This process often requires a conversion factor, which is a numerical multiplier that relates the two units. For example, knowing that 1 m³ is approximately equal to 1.30795 yd³ allows for accurate conversions between these volume units.

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert one set of units to another by multiplying by conversion factors. This method ensures that units cancel appropriately, leading to the desired unit in the final answer. It is a crucial skill in chemistry and physics for ensuring that calculations are dimensionally consistent.