Select All Correct Conversions.A. 343 M = 34.3 Cm 343 \, \text{m} = 34.3 \, \text{cm} 343 M = 34.3 Cm B. 1.25 Km = 1 , 250 M 1.25 \, \text{km} = 1,250 \, \text{m} 1.25 Km = 1 , 250 M C. 4.7 M = 47 , 000 Mm 4.7 \, \text{m} = 47,000 \, \text{mm} 4.7 M = 47 , 000 Mm D. 345 M = 0.345 Km 345 \, \text{m} = 0.345 \, \text{km} 345 M = 0.345 Km E. $1.7

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Introduction

Unit conversions are an essential aspect of mathematics, particularly in physics and engineering. They involve changing the unit of measurement of a quantity from one system to another. In this article, we will explore the correct conversions of various units, including length, distance, and speed.

Length Conversions

Length conversions involve changing the unit of measurement of a quantity from one system to another. There are several types of length conversions, including:

Meter to Centimeter Conversion

The meter (m) is the base unit of length in the International System of Units (SI). The centimeter (cm) is a smaller unit of length, equal to one-hundredth of a meter. To convert meters to centimeters, we multiply the number of meters by 100.

Example: 343 m=343×100=34,300 cm343 \, \text{m} = 343 \times 100 = 34,300 \, \text{cm}

Kilometer to Meter Conversion

The kilometer (km) is a larger unit of length, equal to one thousand meters. To convert kilometers to meters, we multiply the number of kilometers by 1,000.

Example: 1.25 km=1.25×1,000=1,250 m1.25 \, \text{km} = 1.25 \times 1,000 = 1,250 \, \text{m}

Meter to Millimeter Conversion

The millimeter (mm) is an even smaller unit of length, equal to one-thousandth of a meter. To convert meters to millimeters, we multiply the number of meters by 1,000.

Example: 4.7 m=4.7×1,000=4,700 mm4.7 \, \text{m} = 4.7 \times 1,000 = 4,700 \, \text{mm}

Meter to Kilometer Conversion

The kilometer (km) is a larger unit of length, equal to one thousand meters. To convert meters to kilometers, we divide the number of meters by 1,000.

Example: 345 m=345÷1,000=0.345 km345 \, \text{m} = 345 \div 1,000 = 0.345 \, \text{km}

Other Conversions

Other conversions include:

  • Meter to Inch Conversion: To convert meters to inches, we multiply the number of meters by 39.37.
  • Meter to Foot Conversion: To convert meters to feet, we multiply the number of meters by 3.28.
  • Meter to Yard Conversion: To convert meters to yards, we multiply the number of meters by 1.09.

Discussion

Now that we have explored the correct conversions of various units, let's discuss some common mistakes that people make when converting units.

  • Not checking the unit: One common mistake people make is not checking the unit of measurement. For example, if a problem asks for the length in meters, but the answer is given in centimeters, it's likely that the unit was not checked.
  • Not using the correct conversion factor: Another common mistake people make is not using the correct conversion factor. For example, if a problem asks for the length in meters, but the conversion factor used is 1,000 instead of 1,000,000, it's likely that the conversion factor was not used correctly.
  • Not rounding the answer: Finally, people often forget to round the answer to the correct number of significant figures. For example, if a problem asks for the length in meters, but the answer is given as 34,300.123, it's likely that the answer was not rounded correctly.

Conclusion

In conclusion, unit conversions are an essential aspect of mathematics, particularly in physics and engineering. By understanding the correct conversions of various units, we can solve problems more accurately and efficiently. Remember to check the unit of measurement, use the correct conversion factor, and round the answer to the correct number of significant figures.

Answer Key

A. 343 m=34,300 cm343 \, \text{m} = 34,300 \, \text{cm} (Correct) B. 1.25 km=1,250 m1.25 \, \text{km} = 1,250 \, \text{m} (Correct) C. 4.7 m=4,700 mm4.7 \, \text{m} = 4,700 \, \text{mm} (Correct) D. 345 m=0.345 km345 \, \text{m} = 0.345 \, \text{km} (Correct) E. 1.7 km=1,700 m1.7 \, \text{km} = 1,700 \, \text{m} (Incorrect)

Q: What is the difference between a meter and a kilometer?

A: A meter (m) is the base unit of length in the International System of Units (SI), while a kilometer (km) is a larger unit of length, equal to one thousand meters.

Q: How do I convert meters to centimeters?

A: To convert meters to centimeters, you multiply the number of meters by 100.

Q: How do I convert kilometers to meters?

A: To convert kilometers to meters, you multiply the number of kilometers by 1,000.

Q: How do I convert meters to millimeters?

A: To convert meters to millimeters, you multiply the number of meters by 1,000.

Q: How do I convert meters to kilometers?

A: To convert meters to kilometers, you divide the number of meters by 1,000.

Q: What is the conversion factor for meters to inches?

A: The conversion factor for meters to inches is 39.37.

Q: What is the conversion factor for meters to feet?

A: The conversion factor for meters to feet is 3.28.

Q: What is the conversion factor for meters to yards?

A: The conversion factor for meters to yards is 1.09.

Q: How do I round my answer when converting units?

A: When rounding your answer, you should round to the correct number of significant figures. For example, if a problem asks for the length in meters, but the answer is given as 34,300.123, you should round it to 34,300.

Q: What are some common mistakes people make when converting units?

A: Some common mistakes people make when converting units include:

  • Not checking the unit of measurement
  • Not using the correct conversion factor
  • Not rounding the answer to the correct number of significant figures

Q: How do I check the unit of measurement?

A: To check the unit of measurement, you should look at the problem and see what unit is required. For example, if a problem asks for the length in meters, you should make sure your answer is in meters.

Q: How do I use the correct conversion factor?

A: To use the correct conversion factor, you should look at the problem and see what conversion factor is required. For example, if a problem asks for the length in meters, but the conversion factor used is 1,000 instead of 1,000,000, you should use the correct conversion factor.

Q: Why is it important to round my answer when converting units?

A: It is important to round your answer when converting units because it helps to ensure that your answer is accurate and easy to read. Rounding your answer to the correct number of significant figures helps to avoid confusion and ensures that your answer is clear and concise.

Q: Can you give me some examples of unit conversions?

A: Here are some examples of unit conversions:

  • 343 m=34,300 cm343 \, \text{m} = 34,300 \, \text{cm}
  • 1.25 km=1,250 m1.25 \, \text{km} = 1,250 \, \text{m}
  • 4.7 m=4,700 mm4.7 \, \text{m} = 4,700 \, \text{mm}
  • 345 m=0.345 km345 \, \text{m} = 0.345 \, \text{km}
  • 1.7 km=1,700,000 mm1.7 \, \text{km} = 1,700,000 \, \text{mm}

Note: The correct answer for E is 1.7 km=1,700,000 mm1.7 \, \text{km} = 1,700,000 \, \text{mm}, not 1,700 m1,700 \, \text{m}.