Question

A personal trainer uses calipers on a client to determine his percent body fat. After taking the necessary measurements, the personal trainer determines that the client's body contains \(11.2 \%\) fat by mass ( \(11.2 \mathrm{lb}\) of fat per \(100 \mathrm{lb}\) of body mass). If the client weighs \(225 \mathrm{lb}\), how many \(\mathrm{kg}\) of fat does he have?

Short answer

11.43 kg

Step-by-step solution

- Calculate Pounds of Fat

To find out how many pounds of fat the client has, use the given percentage of body fat and the client's total weight. Multiply the total weight by the percentage in decimal form: \[ 225 \text{ lb} \times \frac{11.2}{100} = 25.2 \text{ lb of fat} \]

- Convert Pounds to Kilograms

To convert pounds of fat to kilograms, use the conversion factor: 1 lb = 0.453592 kg. Multiply the pounds of fat by this conversion factor: \[ 25.2 \text{ lb} \times 0.453592 \text{ kg/lb} \ = 11.4314784 \text{ kg of fat} \]

- Round the Result

Round the result to a reasonable number of decimal places (typically two decimal places for body weight): \[ 11.4314784 \text{ kg} \rightarrow 11.43 \text{ kg of fat} \]

Key concepts

percentage calculations

Percentage calculations are a fundamental mathematical concept used to express proportions and changes. In this exercise, the personal trainer determines the client's body fat percentage. The body fat percentage is given as 11.2%. This means that for every 100 pounds of the client's total body mass, 11.2 pounds are fat.

To calculate the actual pounds of fat in the client's body, one must convert the percentage to its decimal form by dividing by 100. Then, multiply this decimal form by the client's total weight:

\[\text{Total Pounds of Fat} = 225 \text{ lb} \times \frac{11.2}{100} = 25.2 \text{ lb of fat}\]

Understanding percentage calculations helps in various real-life situations such as determining discounts while shopping, calculating interest rates, and in this case, assessing body fat.

unit conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another set. This is crucial in scientific measurements and real-world applications where different systems of measurement are used.

In the exercise, the quantity of fat calculated in pounds needs to be converted to kilograms. The conversion factor between pounds and kilograms is:

\[ 1 \text{ lb} = 0.453592 \text{ kg} \]

By multiplying the pounds of fat by this conversion factor, you can convert the fat mass from pounds to kilograms:

\[ 25.2 \text{ lb} \times 0.453592 \text{ kg/lb} = 11.4314784 \text{ kg of fat} \]

Unit conversion ensures that measurements are accurately communicated and interpreted, especially in contexts involving different measurement systems such as medical, scientific, and international settings.

weight measurement

Weight measurement is essential in various fields, from health and fitness to science and engineering. In this example, the client's body weight is a key input required to calculate the amount of body fat.

The client weighs 225 pounds, which serves as the total mass from which the body fat percentage is calculated. Accurate weight measurement allows for precise calculations.

Initially, the body fat in pounds is determined from the given percentage, and then this value is converted to kilograms for a different perspective or specific requirement:

\[ \text{Total Pounds} = 225 \text{ lb} \]
\[ \text{Pounds of Fat} = 25.2 \text{ lb} \]
\[ \text{Kilograms of Fat} = 11.4314784 \text{ kg} \rightarrow 11.43 \text{ kg} \]

Understanding weight measurement allows individuals to track health metrics, manage fitness goals, and perform accurate scientific experiments.