Problem 47 - 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. Sports A high jumper jumps 6 ft 8 in. How many meters is this?

Step-by-Step Solution

Answer

The high jumper's height in meters is approximately 2.03 meters.

Step 1: Convert Feet and Inches to Total Inches

First, convert 6 feet to inches. Since there are 12 inches in a foot, multiply 6 by 12 to get 72 inches. Add the 8 additional inches to this total, giving you 72 + 8 = 80 inches.

Step 2: Convert Inches to Meters

Use the conversion factor that 1 inch is equal to 0.0254 meters. Multiply the total inches by this conversion factor to change inches to meters: \[80 \text{ inches} \times 0.0254 = 2.032 \text{ meters} \]

Step 3: Round the Answer

Round 2.032 meters to the nearest hundredth. The digit in the hundredths place is 3 and the digit following it is 2, so it rounds to 2.03 meters.

Key Concepts

Understanding Inches to Meters Conversion

When converting units from inches to meters, it can be a straightforward process once you know the conversion factor. In this scenario, the conversion factor is that one inch is equal to approximately 0.0254 meters.
To convert inches to meters, you simply multiply the length in inches by 0.0254. This gives you the equivalent measurement in meters directly.

• If you have 80 inches to convert, you calculate: 80 inches × 0.0254 meters/inch = 2.032 meters.
• This conversion factor is universal, so you can confidently use it for any other conversion needs between these two units.

Understanding this conversion factor will help you tackle any problem asking for a switch from inches to meters with ease.

Mastering Rounding Decimals

Rounding decimals is a common and useful skill in mathematics, essential for estimating and simplifying results. When asked to round a number to a specific decimal place, there are some simple steps to follow:
Let's consider the number 2.032, which needs rounding to the nearest hundredth. The hundreds place is the second number after the decimal point. In 2.032, this digit is 3. The next number, in the thousandths place, is 2.

• If this following number (thousandths place) is 5 or greater, increase the hundredths digit by 1.
• If it is less than 5, as in this case, keep the hundredths digit the same.

Thus, 2.032 rounded to the nearest hundredth is 2.03. Rounding helps in creating easy-to-read numbers that are often required for measurements and reporting.

Navigating Measurement Conversion

Measurement conversion is an integral part of dealing with real-world situations, especially when you need to interpret measurements in different systems like imperial and metric.
In many fields, such as sports or construction, being adept at converting measurements ensures accuracy and consistency. In our example with the high jumper, the initial measurement was in feet and inches, a common use case in the United States. However, the global standard is often the metric system, which uses meters.
Here's a helpful way to remember what's involved in converting different types of measurements:

• First, identify the units you need to convert from and to (e.g., feet and inches to meters).
• Use known conversion factors (e.g., 1 inch = 0.0254 meters) to switch between these units.

By regularly practicing such conversions, it becomes second nature, ensuring you can adapt measurements quickly, whether you're dealing with distances, weights, or volumes.