Problem 36 - Prealgebra

Question

Set up the following problems as we have set up the examples in this section. Then use a calculator for the calculations and round your answers to the nearest hundredth. 65 L to gallons

Step-by-Step Solution

Answer

65 liters is approximately 17.17 gallons.

Step 1: Understand the Conversion Factor

To convert from liters to gallons, we need to know the conversion factor. 1 liter is approximately equal to 0.26417 gallons.

Step 2: Multiply by the Conversion Factor

Multiply the amount in liters by the conversion factor to convert to gallons. \[65 \text{ L} \times 0.26417 \text{ gal/L} = 17.17095 \text{ gal}\]

Step 3: Round the Result

Round the calculated result to the nearest hundredth. The result is 17.17095 gallons, which rounds to 17.17 gallons.

Key Concepts

Liters to Gallons

Converting between liters and gallons is a common task, often necessary in fields like science, cooking, and travel where different regions may use different units of measurement. Understanding this conversion can help in comparing and translating quantities.

• A liter (L) is a metric unit of volume commonly used around the world, especially in countries influenced by the metric system.
• A gallon is a unit of volume commonly used in the United States. However, it's important to note that the U.S. gallon differs slightly from the U.K gallon (also known as the imperial gallon).
• In our context, 1 liter is approximately equivalent to 0.26417 U.S. gallons.

Bringing the two units into a common understanding can make communication and calculations much easier, especially when you encounter international data or instructions.

Conversion Factor

The conversion factor is an essential mathematical tool used to switch between different units of measurement. It acts like a bridge, allowing you to translate a quantity from one unit to another seamlessly.

• To convert liters to gallons, we use the specific conversion factor: 1 liter = 0.26417 gallons.
• This factor allows us to determine how many gallons are equivalent to the liters we have. It's a proportionate value that maintains the relationship between the two units.

For example, if you have a quantity measured in liters and need it in gallons, simply multiply by the conversion factor:
\[ ext{Number of gallons} = ext{Number of liters} \times 0.26417 \] Using this method can simplify and speed up many real-world problems and applications.

Rounding Numbers

Rounding is a basic, yet crucial concept in mathematics and everyday life. It helps simplify numbers to make them easier to work with and communicate. When you perform calculations, especially with measures, rounding becomes handy to approximate to a desired degree of accuracy.

• When instructed to round to the nearest hundredth, you are generally keeping two decimal places in your final result.
• In our example of converting 65 liters to gallons, the exact result before rounding was 17.17095 gallons.

To apply rounding properly:

• Look at the third decimal place: if it's 5 or more, round the second decimal up by one. If it's less than 5, keep the second decimal the same.
• For 17.17095, the third decimal is a 0, meaning we keep the second decimal as 17.17.

This is how rounding assists in producing a neat, usable number without excess precision that isn't necessary for most practical uses.