Problem 34 - 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. \(400 \mathrm{mL}\) to cubic inches

Step-by-Step Solution

Answer

400 mL is approximately 24.41 cubic inches.

Step 1: Understand the Conversion Factors

We need to convert from milliliters to cubic inches. It's important to know the conversion factor between these units. There are approximately 0.0610237 cubic inches in 1 milliliter.

Step 2: Set Up the Conversion Calculation

To convert 400 mL to cubic inches, we'll multiply 400 by the conversion factor. The mathematical expression for this conversion is: \[400 \text{ mL} \times 0.0610237 \text{ cubic inches/mL}\]

Step 3: Perform the Calculation Using a Calculator

Use a calculator to multiply 400 by 0.0610237. When calculating: \[ 400 \times 0.0610237 = 24.40948 \] cubic inches.

Step 4: Round the Result

Round the calculated result to the nearest hundredth. The value 24.40948 rounded to the nearest hundredth is 24.41 cubic inches.

Key Concepts

milliliters to cubic inches

Converting measurements from milliliters (mL) to cubic inches can be an essential skill, especially in scientific and engineering contexts where various units of measurement are used. Milliliters are a metric unit of volume, and cubic inches belong to the imperial system. When converting milliliters to cubic inches, it's crucial to use the correct conversion factor. The standard conversion factor is approximately 0.0610237 cubic inches per milliliter. This means that 1 mL is equivalent to 0.0610237 cubic inches. To perform the conversion:

• Multiply the number of milliliters by 0.0610237.
• Ensure you have set up the multiplication properly to reflect the units being converted.

For example, if you have 400 mL, you would calculate the volume in cubic inches by multiplying 400 by 0.0610237, resulting in 24.40948 cubic inches.

rounding numbers

Rounding is a mathematical process used to simplify numbers, making them easier to work with or interpret. When working with decimal numbers, such as those obtained in unit conversions, it is often necessary to round the results to a certain number of decimal places for clarity or precision. In the context of this exercise, we are instructed to round to the nearest hundredth. This means that we look at the third decimal place:

• If the digit in the third decimal place is 5 or above, the second decimal place is rounded up.
• If the digit is less than 5, the second decimal place remains the same.

So, for the calculated result of 24.40948: 1. Look at the digit at the thousandths place (the third decimal place), which is 9. 2. Since 9 is greater than 5, we round the second decimal place, 0, up by one, leading to 24.41.

conversion factors

Conversion factors are vital in the process of changing one set of units to another. They enable you to accurately switch between different measurement scales without altering the actual quantity. A conversion factor is constructed based on the equivalence between two units. In our example of converting milliliters to cubic inches, the conversion factor is 0.0610237 cubic inches per milliliter. This is derived from the known relationship between the two units. To apply a conversion factor:

• Identify the value and units you start with.
• Multiply by the conversion factor suited for those units.
• The resulting calculation gives you the converted value in the desired units.

Conversion factors are not only used in converting volume measurements but are prevalent in various scientific and real-life applications, allowing seamless operation across different systems of measurement.