Question

Convert the following weights in pounds to kilograms (round to the nearest tenth where indicated). \(150 \mathrm{lb}=\) _______ \(\mathrm{kg}\)

Short answer

150 lb is approximately 68.0 kg.

Step-by-step solution

Identify the Conversion Factor

To convert pounds (lb) to kilograms (kg), use the conversion factor: 1 lb = 0.453592 kg.

Apply the Conversion Factor

Multiply the given weight in pounds by the conversion factor. \[ 150 \text{ lb} \times 0.453592 \text{ kg/lb} = 68.0388 \text{ kg} \]

Round to the Nearest Tenth

Round the calculated weight in kilograms to the nearest tenth. Since the digit in the hundredths place is 3, we round down, resulting in 68.0 kg.

Key concepts

Weight Conversion

Weight conversion is a basic concept in math that involves changing the unit of measurement from one system to another. It's useful in many scenarios, such as when traveling to a country that uses a different system or comparing recipes from various parts of the world. One common type of weight conversion is from pounds to kilograms. Knowing how to perform such transformations accurately is important, especially in scientific, health, and engineering fields.

The process hinges on knowing the correct conversion factor, which allows us to multiply or divide by a specific number to change our measurement unit. Through multiplication, we can seamlessly transform weights from the imperial system (pounds) to the metric system (kilograms), ensuring accuracy and consistency in calculations.

Pounds to Kilograms

Converting pounds to kilograms is a standard task in weight conversion, especially since the metric system is widely used around the world. The two systems stem from different historical measurements, with one being used primarily in the U.S. (pounds) and the other internationally (kilograms).

To make this conversion, we'll employ a specific conversion factor we know for these two units: 1 pound is equivalent to approximately 0.453592 kilograms. This number is derived from the precise scientific definition of a kilogram. When converting, always multiply the number of pounds by this factor to obtain the weight in kilograms.

For example, if you have a weight of 150 pounds, the equation would be: \[150 ext{ lb} imes 0.453592 ext{ kg/lb} = 68.0388 ext{ kg}\] Not only does this calculation give an accurate result, but it also forms the basis for understanding larger concepts in conversion and measurement systems.

Rounding Numbers

Rounding numbers is an essential skill, especially in everyday math usage. It involves making a number simpler but keeping its value close to what it was. We often round numbers to make them easier to work with or to meet specific practical requirements like reporting results in a more conventional way.

When converting pounds to kilograms, you may need to round the number after computation due to precision constraints or presentation guidelines. Typically, we round to the nearest tenth, which focuses on the first digit after the decimal point. Here’s a quick guide on how to do it:

• If the digit in the hundredths place is 5 or more, round up the tenths place by one.
• If the digit in the hundredths place is less than 5, keep the tenths place as is.

In our example, the number calculated was 68.0388 kg. Since the digit in the hundredths place is 3, which is less than 5, we round it down, resulting in 68.0 kg. This rounded value is easier to communicate and often sufficient for practical uses.

Conversion Factor

A conversion factor is a constant that allows you to change one set of units to another. It is essential for enabling accurate conversions between units that appear in different measurement systems. A well-known example is the conversion factor used to change pounds to kilograms, which is 1 lb = 0.453592 kg.

Conversion factors comprise ratios that denote how many units of one system equal a unit in the other. These ratios ensure that when you multiply or divide by the conversion factor, you get a mathematically equivalent figure in the desired units.

It's crucial to remember that using the proper conversion factor is vital for maintaining the integrity and precision of measurements. If done correctly, it helps maintain uniformity across industries and borders. This practice is not just limited to weight but applies to length, volume, temperature, and other types of measurements.