Question

Complete the following volume equivalents: (a) \(1 \mathrm{~L}=? \mathrm{~mL}\) (b) \(1 \mathrm{~L}=? \mathrm{~cm}^{3}\)

Short answer

1 L = 1000 mL and 1 L = 1000 cm³.

Step-by-step solution

Relate Liters to Milliliters

Understand that in the metric system, volume is commonly measured in liters and milliliters. By definition, 1 liter (L) is equivalent to 1000 milliliters (mL). This conversion is based on the metric system's prefix 'milli-', which means one-thousandth. Therefore, since 1 L are 1000 times a milliliter, you get: \(1 \, \mathrm{L} = 1000 \, \mathrm{mL}\).

Relate Milliliters to Cubic Centimeters

In the metric system, volume can also be expressed in cubic centimeters (cm³). It is defined that 1 milliliter (mL) is exactly equal to 1 cubic centimeter (cm³). Thus, the two units are interchangeable, especially in the context of volume measurement for liquids. This equivalence gives you:\(1 \, \mathrm{mL} = 1 \, \mathrm{cm^3}\).

Relate Liters to Cubic Centimeters

Knowing that 1 liter equals 1000 milliliters (from Step 1) and that each milliliter is equal to 1 cubic centimeter (from Step 2), you can now find how many cubic centimeters are in a liter by combining both relationships. This yields:\(1 \, \mathrm{L} = 1000 \, \mathrm{mL} = 1000 \, \mathrm{cm^3}\).

Key concepts

Metric System

The Metric System is an international decimal-based system of measurement that is used universally for scientific and everyday purposes. It offers simplicity and ease in converting between units because all conversions are based on multiples of ten.
One of the primary benefits of the metric system is its use of base units and prefixes to convey quantities. For volume, the basic unit is the liter (L), but there are also smaller units like the milliliter (mL), and related units such as the cubic centimeter (cm³). Importantly, these units interrelate with a factor of ten, which makes calculations straightforward.

• The base unit for volume is the liter.
• The prefix 'milli-' indicates one-thousandth, applicable as a conversion factor.
• Units can be easily converted by moving the decimal point.

The focus on ease and accessibility is why the metric system is preferred in most of the world, especially in scientific contexts.

Liter to Milliliter Conversion

Understanding the conversion between liters and milliliters is essential for tackling volume measurements. In the metric system, direct conversions are easily achieved because of its structured use of prefixes. The prefix 'milli-' signifies that milliliters are a smaller unit than liters.
To convert liters to milliliters, consider these key points:

• 1 liter is equivalent to 1000 milliliters.
• The conversion is based on the 1-to-1000 ratio, due to 'milli-' meaning one-thousandth.
• This relationship simplifies conversions whenever you need to move between these two units by multiplying or dividing by 1000.

For example, if you have 2 liters, you can convert it to milliliters by multiplying: \[ 2 imes 1000 = 2000 \, \text{mL} \] This method of conversion is reliable and can also be smoothly reversed when necessary.

Cubic Centimeter

A cubic centimeter (cm³) is a unit of volume in the metric system. It is equivalent to one milliliter of liquid, which connects solid and liquid measurements seamlessly.
This unit is especially useful in scientific and medical fields where precise volume measurements are needed.
To fully understand cubic centimeters, keep in mind:

• 1 cubic centimeter is symbolized as 1 cm³.
• Cubic centimeters equate directly to milliliters, allowing easy interchange between the units: \(1 \, \text{cm}^3 = 1 \, \text{mL} \).
• Due to their equivalency, they both serve in measuring volume for both solids and liquids.

This equivalence is why you will often hear these measurements used interchangeably in scientific scenarios, offering clarity and simplicity for understanding volume conversions.