Problem 32 - 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. \(100 \mathrm{mi}\) to kilometers

Step-by-Step Solution

Answer

100 miles is approximately 160.93 kilometers.

Step 1: Understand the Conversion Factor

To convert miles to kilometers, we need to use the conversion factor where 1 mile is approximately equal to 1.60934 kilometers. Knowing this factor is vital for setting up the conversion correctly.

Step 2: Set Up the Conversion Equation

Start by writing the given value and multiply it by the conversion factor. The expression to convert miles to kilometers is: \[ 100 \text{ mi} \times \frac{1.60934 \text{ km}}{1 \text{ mi}} \] Here, you multiply 100 miles by the conversion factor 1.60934 km/mi.

Step 3: Perform the Calculation

Using a calculator, multiply 100 by 1.60934. This operation is shown as: \[ 100 \times 1.60934 = 160.934 \] This calculation gives the number of kilometers equivalent to 100 miles.

Step 4: Round the Result

The question asks for the answer to be rounded to the nearest hundredth. The number 160.934 rounded to the nearest hundredth is 160.93 km.

Key Concepts

Unit Conversion

Unit conversion is a common task in mathematics, especially when working with different measurement systems. Think of it as translating from one language to another, where units represent the words. In our example, we are translating miles (mi) to kilometers (km).

### Conversion Factor The key to successful unit conversion lies in the **conversion factor**, which acts as the "translation guide." For miles to kilometers, the conversion factor is approximately 1.60934. It means that 1 mile equals 1.60934 kilometers. This factor is used to convert values by multiplying it with the distance in miles.
### Setting Up the Conversion Equation Set up the equation by multiplying the initial value by the conversion factor:

• Write the initial measurement (e.g., 100 mi)
• Multiply it by the conversion factor expressed as a fraction: \( \frac{1.60934 \, \text{km}}{1 \, \text{mi}} \)

This setup allows you to cancel out the initial unit, leaving only the desired unit of measure.

Calculator Usage

Using a calculator makes math problems involving multiple digits easier and faster. When performing operations like multiplication, a calculator ensures accuracy, especially with long decimals.

### Performing the Calculation After setting up the conversion equation, you are ready to calculate.

• Enter the number to be converted (e.g., 100)
• Multiply this by the conversion factor (e.g., 1.60934)

In this scenario, you would input: 100, then multiply by 1.60934, resulting in a product of 160.934. Calculators help ensure you don't make errors when handling decimals, which are common when doing such conversions.

Rounding Numbers

Rounding is important when you need a simpler, more readable number that still accurately represents the original value. For this situation, we're asked for an answer rounded to the nearest hundredth.

### Understanding Place Values Here, the **hundredth's place** is located two digits to the right of the decimal point. Observing this space is critical when rounding.

• In the number 160.934, the digit in the hundredth place is 3 and the thousandth place is 4.

### Rounding Rules To correctly round a number:

• If the digit in the place to the right (thousandth place) is 5 or more, you increase the digit in the hundredth's place by 1.
• If it's less than 5, keep the digit in the hundredth's place the same.

For 160.934, since 4 is less than 5, we keep the 3, giving us 160.93.