Question

Convert the following weights in pounds to kilograms (round to the nearest tenth where indicated). \(78 \mathrm{lb}=\) _______ \(\mathrm{kg}\)

Short answer

78 lb = 35.4 kg.

Step-by-step solution

Understanding the Conversion Factor

To convert pounds (lb) to kilograms (kg), you need to know the conversion factor. 1 pound is approximately equal to 0.45359237 kilograms.

Setting Up the Conversion Equation

Write down the conversion equation: \( \text{{weight in kg}} = \text{{weight in lb}} \times 0.45359237 \). For this exercise, the weight in pounds is 78.

Calculating the Weight in Kilograms

Substitute the given weight into the equation: \( 78 \times 0.45359237 \). Perform the multiplication to find the weight in kilograms.

Rounding to the Nearest Tenth

The result of the multiplication is approximately 35.38003706. Round this number to the nearest tenth. The tenth place is the digit right after the decimal point, which is 3. Since the digit in the hundredth place is 8 (which is 5 or greater), round up the 3 to 4.

Key concepts

Pound to Kilogram Conversion

Converting weights from pounds to kilograms is a common task in mathematics and science. It allows you to work with a standardized unit of mass used worldwide. To perform this conversion, we need to use a specific conversion factor.

The conversion factor between pounds and kilograms is 0.45359237. This means that 1 pound is equivalent to approximately 0.45359237 kilograms. When you need to convert pounds to kilograms, you multiply the weight in pounds by this conversion factor to find the weight in kilograms.

• Multiply the pounds by 0.45359237 to convert to kilograms.
• For example, for 78 pounds: calculate 78 x 0.45359237.
• This will give you the weight in kilograms.

Understanding and using the conversion factor correctly is crucial for accurate measurement conversions in various scientific and practical applications.

Mathematical Rounding

Mathematical rounding is an essential skill, especially when dealing with decimal numbers. It simplifies numbers while maintaining their approximate value, which is useful for easy interpretation and making quick calculations.

When rounding to the nearest tenth, we focus on the number located in the tenths place, which is the first digit to the right of the decimal point. The rounding rules are straightforward:

• If the digit in the hundredths place (the second digit right after the decimal) is 5 or more, we round the tenths digit up.
• If the hundredths digit is less than 5, we leave the tenths digit as it is.

For our exercise, we obtained a weight of approximately 35.38003706 kilograms. To round to the nearest tenth:

• Look at the hundredths digit, which is 8.
• Since 8 is greater than 5, we increase the tenths digit (3) to 4.

Thus, 35.38003706 rounds to 35.4 kilograms.

Conversion Factor Calculation

Calculating with a conversion factor involves understanding and applying the correct multiplier to transition between units. Here, the conversion factor helps convert pounds to kilograms accurately.

In any conversion scenario, it's crucial to know the accurate conversion factor. This is a constant value, not a variable, and ensures the conversion retains correct proportions between units.

• Always verify the conversion factor for accuracy. In this case, it is 0.45359237 for pounds to kilograms.
• Multiply the original measurement by this factor to find the equivalent measurement in the new unit.
• For example, converting 78 pounds requires a calculation of 78 multiplied by 0.45359237.
• This results in the equivalent weight in kilograms.

Mastering the use of conversion factors is pivotal for anyone regularly dealing with different measurement systems.