Question

Perform the following unit conversions. a. Congratulations! You and your spouse are the proud parents of a new baby, born while you are studying in a country that uses the metric system. The nurse has informed you that the baby weighs 3.91 kg and measures 51.4 cm. Convert your baby’s weight to pounds and ounces and her length to inches (rounded to the nearest quarter inch). b. The circumference of the earth is 25,000 mi at the equator. What is the circumference in kilometers? in meters? c. A rectangular solid measures 1.0 m by 5.6 cm by 2.1 dm. Express its volume in cubic meters, liters, cubic inches, and cubic feet.

Short answer

a. The baby's weight is approximately 8 pounds and 9.90 ounces, and the baby's length is 20.25 inches. b. The Earth's circumference is 40,233.5 kilometers or 40,233,500 meters at the equator. c. The volume of the rectangular solid is 0.01176 cubic meters, 11.76 liters, 717.61 cubic inches, and 0.41524 cubic feet.

Step-by-step solution

Conversion factors

For the baby's weight, we'll use the conversion factor of 1 kg = 2.20462 pounds. To convert from kilograms to pounds and ounces, we need to know that 1 pound = 16 ounces. For the baby's length, we'll use the conversion factor of 1 inch = 2.54 cm.

Convert weight to pounds and ounces

To convert the baby's weight from kilograms to pounds, we will multiply the given weight in kilograms by the conversion factor. Weight in pounds = 3.91 kg * 2.20462 lb/kg = 8.61896 lb Now, to convert the remaining decimals to ounces, we'll multiply it by 16: Weight in ounces = 0.61896 lb * 16 oz/lb = 9.90336 oz Thus, the baby's weight is 8 pounds and approximately 9.90 ounces.

Convert length to inches

To convert the baby's length from centimeters to inches, we will multiply the given length in centimeters by the conversion factor. Length in inches = 51.4 cm * (1 in / 2.54 cm) = 20.23622 in We'll round this to the nearest quarter inch, so the baby's length becomes 20.25 inches. b. Circumference of Earth in kilometers and meters:

Conversion factors

To convert the Earth's circumference from miles to kilometers and meters, we will use the conversion factors: 1 mile = 1.60934 kilometers and 1 kilometer = 1000 meters.

Convert circumference to kilometers

Circumference in kilometers = 25,000 miles * 1.60934 km/mi = 40,233.5 km

Convert circumference to meters

Circumference in meters = 40,233.5 km * 1000 m/km = 40,233,500 m c. Volume of rectangular solid in different units:

Convert all dimensions to meters

We need to convert all dimensions of the rectangular solid to meters. Width = 1.0 m Length = 5.6 cm * (1 m / 100 cm) = 0.056 m Height = 2.1 dm * (1 m / 10 dm) = 0.21 m

Calculate volume in cubic meters

Volume in cubic meters = Width × Length × Height = 1.0 m × 0.056 m × 0.21 m = 0.01176 m³

Convert volume to liters

Volume in liters = 0.01176 m³ * (1000 L / 1 m³) = 11.76 L

Convert volume to cubic inches

To convert the volume to cubic inches, we can use the conversion factor 1 m³ = 61,023.7 in³. Volume in cubic inches = 0.01176 m³ * 61,023.7 in³/m³ = 717.60885 in³

Convert volume to cubic feet

To convert the volume to cubic feet, we can use the conversion factor 1 m³ = 35.3147 ft³. Volume in cubic feet = 0.01176 m³ * 35.3147 ft³/m³ = 0.41524 ft³

Key concepts

Metric System

The metric system is an internationally recognized system for measuring. It is based on powers of ten, making it easy to use and convert between units. For example, common units for length are meters (m), centimeters (cm), and kilometers (km). Units for volume and weight include liters (L) and kilograms (kg), respectively. This system uses a simple structure: each unit type has a base unit, and prefixes are added to indicate multiples or fractions of the base unit, such as centi- (one hundredth), deci- (one tenth), and kilo- (one thousand).

The ease of conversion between units within the metric system is one of its greatest strengths, especially for educational and scientific purposes.

Conversion Factors

Conversion factors are the numerical values used to switch between different units of measure. Understanding and using conversion factors correctly is crucial for accurate unit conversions. For example, to convert weight from kilograms to pounds, we use the conversion factor 1 kg = 2.20462 pounds. Similarly, 1 mile equals 1.60934 kilometers. These factors serve as a bridge to go from one unit of measurement to another and are derived from established equivalences between different measurement systems.

Here are a few important conversion factors you need to know:

• 1 kg = 2.20462 pounds
• 1 inch = 2.54 centimeters
• 1 mile = 1.60934 kilometers
• 1 m³ = 1000 liters

It is helpful to remember these commonly used factors or have them readily available when performing conversions.

Measurement Units

Understanding different measurement units is key to interpreting and converting various quantities. In the metric system:

• Length is typically measured in meters (m), centimeters (cm), or kilometers (km).
• Mass is commonly measured in kilograms (kg) or grams (g).
• Volume is often measured in cubic meters (m³) or liters (L).

In contrast, the imperial system uses units such as inches (in), feet (ft), and pounds (lb). Each measurement system has its own set of units, and understanding them is essential for proper conversion and comparison between systems. For instance, to convert centimeters to inches, you use the conversion factor 1 inch = 2.54 cm.

By understanding these units, we can make accurate conversions and understand quantities better across different systems.

Volume Calculation

Volume calculation involves determining the amount of space an object occupies. In three-dimensional space, volume can be calculated by multiplying the dimensions of an object. For a rectangular solid, which might have dimensions measured in meters, centimeters, or decimeters, the volume formula is:\[ \text{Volume} = \text{Width} \times \text{Length} \times \text{Height} \]Converting this volume to different units involves additional conversion factors, such as from cubic meters to liters (1 m³ = 1000 L) or cubic inches to centimeters. This calculation is crucial in fields ranging from engineering to fluid dynamics where precise measurement of space and capacity is required.

When performing volume calculations, always ensure units are consistent, or apply correct conversion factors to maintain accuracy in results.