Question

A roller coaster requires riders to be at least 48 inches tall. Given that there are approximately $2.54$ centimeters in an inch, how tall must a rider be to the nearest whole centimeter to ride the roller coaster? (A) 96 (B) 122 (C) 148 (D) 190

Short answer

The rider must be at least 122 cm tall.

Step-by-step solution

Understand the Conversion

To convert inches to centimeters, we need to use the conversion factor where 1 inch is approximately 2.54 centimeters. We apply this factor to the height requirement given in inches.

Set Up the Equation

Let's set up an equation to convert 48 inches to centimeters using the conversion factor: $$48\text{ inches}\times 2.54\text{ cm/inch}=x\text{ cm}$$ where $x$ is the height in centimeters.

Perform the Calculation

Calculate the number of centimeters by multiplying the inches by the conversion factor:$$x=48\times 2.54=121.92\text{ cm}$$

Round the Result

Since we need the height to the nearest whole centimeter, we round 121.92 to the nearest whole number, which gives us 122 cm.

Key concepts

Unit Conversion

Unit conversion is a fundamental concept in many mathematical and scientific applications. It involves changing a measurement from one unit to another while maintaining the same quantity. This is crucial when dealing with different measurement systems, such as converting inches to centimeters. In our example, we need to convert a height from inches to centimeters.
To accomplish this, we use a conversion factor. The conversion factor tells us how many units of the outcome measurement are equal to one unit of the initial measurement. In this case, 1 inch is approximately equal to 2.54 centimeters.
When we convert 48 inches into centimeters, we multiply 48 by 2.54. This process ensures that we're maintaining the correct quantity in a different unit, resulting in the calculation of the height being 121.92 centimeters.

Height Measurement

Height measurement is often required in various scenarios, such as determining eligibility for activities like riding roller coasters. In these cases, accuracy in measurements is key to ensure safety and compliance with guidelines.
Height can be measured in several units, including inches and centimeters. Inches are commonly used in the United States, while centimeters are more prevalent in many other countries. When a situation arises where the measurement is given in inches but needs interpretation in centimeters, unit conversion must be applied.
Understanding the equivalency between these units is important, as seen in our example where 48 inches needed to be converted to centimeters to determine if the height exceeds the 122 cm requirement. This ensures that the measurement is applicable to different contexts and standards globally.

Rounding Numbers

Rounding numbers is an essential skill in mathematics, particularly when precision is less crucial, and a whole number is required for simplicity or context. It's a method of approximating a number to make it easier to work with, often to the nearest whole number or specified place value.
For example, when rider height was calculated as 121.92 cm, it needed to be rounded to the nearest whole centimeter. The rule for rounding is simple: if the digit in the tenths place is five or greater, you round up the preceding digit. If it's less than five, you round down.
In this exercise, 121.92 becomes 122 because the 9 in the tenths place means you round up the 1 in the ones place, resulting in a rounded value fit for practical usage.

Mathematical Calculations

Mathematical calculations involve performing operations according to mathematical rules to find solutions to problems. In solving the roller coaster height problem, a straightforward multiplication followed by rounding is required.
The process began with setting up an equation to convert inches to centimeters: $$x=48\times 2.54$$This equation is a multiplication of a given value by a conversion factor, a fundamental calculation. After multiplying 48 by 2.54, the result is a decimal number, 121.92. This result needs further processing, revealing the necessity to apply rounding.
Calculations like these are common in daily life, as they help convert and simplify measurements, making complex data more understandable and applicable.