Problem 3 - College Physics

Question

Convert the following: (a) 40000000 bytes to MB, (b) \(0.5722 \mathrm{~mL}\) to \(\mathrm{L}\), (c) \(2.684 \mathrm{~m}\) to \(\mathrm{cm},\) and (d) 5500 bucks to kilobucks.

Step-by-Step Solution

Answer

(a) 40 MB, (b) 0.0005722 L, (c) 268.4 cm, (d) 5.5 kilobucks.

Step 1: Convert bytes to MB

To convert bytes to megabytes (MB), we need to divide by the conversion factor of 1 MB = 1,000,000 bytes. Thus, we perform the following calculation: \[ 40000000 \text{ bytes} \div 1000000 = 40 \text{ MB} \].

Step 2: Convert mL to L

To convert milliliters (mL) to liters (L), we need to divide by 1,000, since 1 L = 1,000 mL. Using the given value, the conversion is: \[ 0.5722 \text{ mL} \div 1000 = 0.0005722 \text{ L} \].

Step 3: Convert meters to centimeters

To convert meters (m) to centimeters (cm), we multiply by 100, as 1 m = 100 cm. Thus, we calculate: \[ 2.684 \text{ m} \times 100 = 268.4 \text{ cm} \].

Step 4: Convert bucks to kilobucks

To convert bucks to kilobucks, divide by 1,000, because 1 kilobuck = 1,000 bucks. So, the conversion is: \[ 5500 \text{ bucks} \div 1000 = 5.5 \text{ kilobucks} \].

Key Concepts

Bytes to Megabytes

When converting bytes to megabytes (MB), we focus on understanding the conversion factor. Bytes are the basic unit of digital information. However, for larger files, measuring in bytes can become unwieldy. That's where megabytes come in.

• Conversion Factor: 1 MB equals 1,000,000 bytes. We use this conversion factor to easily switch between the two units.
• Example Conversion: If you have 40,000,000 bytes, to find out how many MB this is, you divide by 1,000,000. The calculation is: \( 40,000,000 \div 1,000,000 = 40 \text{ MB} \).
• Why the Conversion? Megabytes simplify communication of file sizes, making it easier to understand data limits and storage capacities.

Milliliters to Liters

Converting milliliters (mL) to liters (L) is a common task in science and everyday tasks. It helps in accurately measuring liquid for activities like cooking or scientific experiments.

• Conversion Factor: 1 liter equals 1,000 milliliters. This fundamental step is crucial for converting smaller liquid measures into comprehensible larger units.
• Example Conversion: For 0.5722 mL, divide by 1,000 to find the equivalent in liters: \( 0.5722 \div 1,000 = 0.0005722 \text{ L} \).
• Practical Implications: This conversion is invaluable in labs and kitchens where precise measurements impact outcomes significantly.

Meters to Centimeters

The conversion from meters to centimeters is essential in everyday measurements, especially in fields such as construction and tailoring.

• Conversion Factor: 1 meter is equal to 100 centimeters. This means multiplying the number in meters by 100 gives you centimeters.
• Example Conversion: Converting 2.684 meters entails multiplying by 100, resulting in: \( 2.684 \times 100 = 268.4 \text{ cm} \).
• Practical Uses: These conversions are pivotal in ensuring accuracy when detailed measurement is key, such as cutting fabric or assessing room dimensions.

Bucks to Kilobucks

Converting bucks to kilobucks can be a handy when dealing with large sums of money, such as in budgeting or economic reports.

• Conversion Factor: 1 kilobuck equals 1,000 bucks. By using this factor, large amounts are expressed in kilobucks, simplifying monetary discussions.
• Example Conversion: If you have 5,500 bucks and want to express this in kilobucks, divide by 1,000: \( 5,500 \div 1,000 = 5.5 \text{ kilobucks} \).
• Relevance: Using kilobucks makes it straightforward to discuss finances in a more digestible format, emphasizing the enormity or simplicity of financial plans.