Question

Express each quantity in a more appropriate unit. There may be more than one acceptable answer. a) \(0.000000345 \mathrm{~m}^{3}\) b) \(47,000,000 \mathrm{~mm}^{3}\) c) \(0.00665 \mathrm{~L}\)

Short answer

a) 0.345 cm³, b) 0.047 m³, c) 6.65 mL

Step-by-step solution

Convert cubic meters to cubic centimeters.

To convert from cubic meters to cubic centimeters, use the conversion factor: 1 cubic meter (m³) = 1,000,000 cubic centimeters (cm³).Thus, multiply the given volume: \(0.000000345 \text{ m}^3 \times 1,000,000 = 0.345 \text{ cm}^3\).

Convert cubic millimeters to cubic meters.

To convert from cubic millimeters to cubic meters, use the conversion factor: 1 cubic meter (m³) = \(1,000,000,000\) cubic millimeters (mm³).Thus, divide the given volume: \(47,000,000 \text{ mm}^3 \div 1,000,000,000 = 0.047 \text{ m}^3\).

Convert liters to milliliters.

To convert from liters to milliliters, use the conversion factor: 1 liter (L) = 1,000 milliliters (mL).Thus, multiply the given volume: \(0.00665 \text{ L} \times 1,000 = 6.65 \text{ mL}\).

Key concepts

Cubic Meters to Cubic Centimeters

When converting cubic meters to cubic centimeters, understanding the basic conversion factor is essential. One cubic meter (m³) is equal to 1,000,000 cubic centimeters (cm³). This means that if you have a volume measured in cubic meters, you can convert it to cubic centimeters by multiplying it by 1,000,000.

This is because each cubic meter is made up of 1,000,000 tiny cubes that measure 1 centimeter on each side. When converting from m³ to cm³, you are essentially filling that large volume with many smaller cubic centimeter blocks. Here is a simple guide to this conversion:

• Identify the volume in cubic meters: for example, 0.000000345 m³.
• Multiply the volume by 1,000,000.
• The result is the volume in cubic centimeters: 0.345 cm³.

Remember, using the conversion factor makes the process straightforward and ensures that your volume is correctly represented in the smaller unit of cubic centimeters.

Cubic Millimeters to Cubic Meters

When converting from cubic millimeters to cubic meters, you'll need to understand the much larger conversion scale between these two units. One cubic meter equals 1,000,000,000 cubic millimeters. Converting mm³ to m³ involves dividing your original volume by this large number.

This conversion is a common necessity in scientific and engineering tasks, requiring a clear understanding of the scale involved. Using this conversion factor, you simplify the conceptual giant leap from the tiny cubic millimeter to the much larger cubic meter. Here's how you can do it:

• Determine the volume in cubic millimeters: 47,000,000 mm³, in this case.
• Divide the volume by 1,000,000,000.
• The result is the volume in cubic meters: 0.047 m³.

This process breaks down the volume into the vast space that a cubic meter represents, simplifying what is initially a significantly smaller measure.

Liters to Milliliters

Converting liters to milliliters is a straightforward and easy process since these units are part of the same metric system of measurements. One liter is exactly equivalent to 1,000 milliliters, meaning conversion is just a matter of multiplying by 1,000.

This conversion is frequently encountered in everyday situations like cooking or science experiments. Having a clear understanding of the 1:1,000 relationship can help you quickly and accurately change volumes from one to the other. Here's how it works:

• Start with the volume in liters: 0.00665 L for instance.
• Multiply by 1,000 to convert to milliliters.
• You will get the volume in milliliters: 6.65 mL.

The simplicity of this conversion makes it especially handy for practical purposes, ensuring clarity and accuracy in volume measurement.