Question

Perform the following metric-English conversions. (a) 72 in. to \(m\) (b) 175 lb to kg (c) \(0.500 \mathrm{qt}\) to \(\mathrm{L}\) (d) \(4.55 \times 10^{-4} \mathrm{~min}\) to ds

Short answer

(a) 1.83 m, (b) 79.38 kg, (c) 0.4732 L, (d) 0.273 ds.

Step-by-step solution

Convert Inches to Meters

To convert inches to meters, use the conversion factor: 1 inch = 0.0254 meters. Multiply 72 inches by this conversion factor: \[72 \text{ inches} \times 0.0254 \text{ meters/inch} = 1.8288 \text{ meters}\] Therefore, 72 inches is 1.8288 meters.

Convert Pounds to Kilograms

To convert pounds to kilograms, use the conversion factor: 1 pound = 0.453592 kilograms. Multiply 175 pounds by this conversion factor: \[175 \text{ pounds} \times 0.453592 \text{ kg/pound} = 79.3786 \text{ kg}\] Therefore, 175 pounds is approximately 79.38 kilograms.

Convert Quarts to Liters

To convert quarts to liters, use the conversion factor: 1 quart = 0.946353 liters. Multiply 0.500 quarts by this conversion factor: \[0.500 \text{ quarts} \times 0.946353 \text{ liters/quart} = 0.473177 \text{ liters}\] Therefore, 0.500 quarts is approximately 0.4732 liters.

Convert Minutes to Deciseconds

First, know that 1 minute = 60 seconds and 1 second = 10 deciseconds. Multiply the time in minutes by the number of seconds per minute, and then convert seconds to deciseconds:\[4.55 \times 10^{-4} \text{ minutes} \times 60 \text{ seconds/minute} = 2.73 \times 10^{-2} \text{ seconds}\]\[2.73 \times 10^{-2} \text{ seconds} \times 10 \text{ deciseconds/second} = 0.273 \text{ ds}\]Therefore, \(4.55 \times 10^{-4}\) minutes is 0.273 deciseconds.

Key concepts

Inches to Meters Conversion

The process of converting inches to meters involves understanding the relationship between these two units of measure. An inch is a unit from the English, or imperial, system, whereas meters are used in the metric system. To make this conversion, a consistent conversion factor is applied: 1 inch equals 0.0254 meters. This means for every inch, you will have 0.0254 meters when converted. To convert inches to meters, simply multiply the number of inches by the conversion factor. For example, if you have 72 inches, you multiply it by 0.0254 to get approximately 1.8288 meters.

• Conversion Factor: 1 inch = 0.0254 meters
• Example Conversion: 72 inches * 0.0254 m/inch = 1.8288 meters

Through this straightforward multiplication, you can easily transition from the imperial to the metric unit, allowing for universal understanding and use.

Pounds to Kilograms Conversion

Converting pounds to kilograms is a common task that involves moving from the imperial system to the metric system. One pound is equivalent to 0.453592 kilograms. This conversion factor enables precise translations between the two units. When you need to convert pounds to kilograms, you multiply the weight in pounds by 0.453592. For example, converting 175 pounds involves calculating 175 times 0.453592, resulting in approximately 79.38 kilograms.

• Conversion Factor: 1 pound = 0.453592 kilograms
• Example Conversion: 175 pounds * 0.453592 kg/pound = 79.38 kilograms

This process allows you to accurately convert weights, simplifying communication of weight measurements internationally.

Quarts to Liters Conversion

Quarts are used primarily in the United States as a liquid volume measure, while liters are part of the metric system, widely accepted globally. This can often require conversions, especially in contexts involving scientific data or international recipes. To convert quarts to liters, use the conversion factor where 1 quart equals 0.946353 liters. Take the number of quarts and multiply it by this factor to determine the equivalent volume in liters. For example, 0.500 quarts times 0.946353 results in approximately 0.4732 liters.

• Conversion Factor: 1 quart = 0.946353 liters
• Example Conversion: 0.500 quarts * 0.946353 liters/quart = 0.4732 liters

This conversion is especially useful when dealing with international culinary instructions or scientific experiments.

Minutes to Deciseconds Conversion

The conversion from minutes to deciseconds involves moving from a larger time unit to a smaller metric unit, offering more precise measurements. First, remember that 1 minute equals 60 seconds, and each second contains 10 deciseconds. To perform the conversion, first transform the minutes into seconds by multiplying by 60. Then, convert the seconds into deciseconds by multiplying by 10. For instance, if you want to convert 4.55 x 10^-4 minutes, first multiply by 60 to get seconds, then by 10 for deciseconds, resulting in 0.273 deciseconds.

• Conversion Steps: 1 minute = 60 seconds, 1 second = 10 deciseconds
• Example Conversion: 4.55 x 10^-4 minutes = 0.273 deciseconds

This two-step process helps in achieving a finer resolution of time, which is beneficial in areas such as scientific research or high-precision engineering.