Question

Given that \(1 \mathrm{~L}=1000 \mathrm{~cm}^{3},\) determine what conversion factor is appropriate to convert \(350 \mathrm{~cm}^{3}\) to liters; to convert \(0.200 \mathrm{~L}\) to cubic centimeters.

Short answer

To convert 350 cm³ to liters, use the given conversion factor, which is 1 L = 1000 cm³. Multiply 350 cm³ by the fraction \(\frac{1 \mathrm{L}}{1000 \mathrm{cm}^3}\), resulting in 0.35 L. To convert 0.200 L to cm³, multiply 0.200 L by the fraction \(\frac{1000 \mathrm{cm}^3}{1 \mathrm{L}}\), resulting in 200 cm³.

Step-by-step solution

Conversion factor from cm³ to L

First, we are going to convert 350 cm³ to liters. For this, we have to use the given conversion factor, which is 1 L = 1000 cm³. To do so, we will set up a fraction that cancels out the cm³ unit and leaves us with L.

Convert 350 cm³ to L

To convert 350 cm³ to L, we will set up the following fraction: \[ \frac{350 \mathrm{~cm}^3}{1} \times \frac{1 \mathrm{~L}}{1000 \mathrm{~cm}^3} \] Now, the cm³ units will cancel each other out, and we will be left with L.

Calculate the equivalent value in L

Multiplying the fractions, we get: \[ \frac{350}{1} \times \frac{1}{1000} \mathrm{~L} = \frac{350}{1000} \mathrm{~L} \] Simplifying the fraction, we get: \[ \frac{350}{1000} \mathrm{~L} = 0.35 \mathrm{~L} \] So, 350 cm³ is equal to 0.35 L.

Conversion factor from L to cm³

Next, we are going to convert 0.200 L to cubic centimeters. For this, we have to use the given conversion factor, which is 1 L = 1000 cm³.

Convert 0.200 L to cm³

To convert 0.200 L to cm³, we will set up the following fraction: \[ \frac{0.200 \mathrm{~L}}{1} \times \frac{1000 \mathrm{~cm}^3}{1 \mathrm{~L}} \] Now, the L units will cancel each other out, and we will be left with cm³.

Calculate the equivalent value in cm³

Multiplying the fractions, we get: \[ \frac{0.200}{1} \times \frac{1000}{1} \mathrm{~cm}^3 = 200 \mathrm{~cm}^3 \] So, 0.200 L is equal to 200 cm³.

Key concepts

Unit Conversion

Understanding unit conversion is crucial for measuring and comparing quantities in different units. In mathematics and science, we often deal with an array of measurement units for length, volume, weight, and more. To make consistent comparisons or calculations, we must be able to convert from one unit to another using a conversion factor.

A conversion factor is a multiplier that allows a quantity expressed in one unit to be converted into an equivalent quantity in another unit. To do this accurately, we need a known relationship between the two units—for example, knowing that 1 liter is equal to 1000 cubic centimeters (cm³). When we set up a conversion factor, we ensure that the units we want to convert from are cancelled out, leaving us with the desired units. This process ensures that the physical quantity remains the same, even though it might be expressed in a different unit of measure.

Cubic Centimeters to Liters

Converting cubic centimeters (cm³) to liters (L) is a task that comes up frequently in fields requiring volume measurements, such as chemistry, cooking, and engineering. The cubic centimeter is a unit of volume in the metric system that represents the volume of a cube with sides of 1 centimeter each. A liter is a larger unit of volume commonly used for measuring liquids and is equivalent to 1,000 cubic centimeters.

To convert from cubic centimeters to liters, we divide the number of cubic centimeters by 1,000. Conversly, to convert liters to cubic centimeters, we multiply the number of liters by 1,000. It's essential to remember that when converting between these two metric units, the conversion factor is based on the relationship that 1 L equals 1,000 cm³. This knowledge allows for precise and straightforward conversions between volumes, like determining the capacity of a water bottle in liters when given in cubic centimeters, or figuring out how much soda to buy for a party in liters rather than cm³.

Conversion Factors

Conversion factors play a vital role in unit conversions. These factors are ratios that express the number of one unit in relation to another and are used as a tool for converting quantities without changing the underlying value. Speaking about volume, especially when delving into smaller or larger volumes, proper conversion factors ensure accurate and usable results.

When we think about conversion factors between cubic centimeters and liters, we always resort to the fundamental relationship: 1 L equals 1,000 cm³. For converting other units of volume, like gallons to liters or milliliters to cubic inches, knowing the relevant conversion factors is key to correct measurements. Being able to manipulate and apply these factors can make complex calculations in fields such as physics, chemistry, and everyday tasks much more manageable. Remembering the correct conversion factors and how to apply them can be the difference between success and error in various applications.