Question

Boston and New York City are 190 miles apart. What is this distance in kilometers? in meters? in feet?

Short answer

The distance between Boston and New York City is approximately 305.78 kilometers, 305,776 meters, and 1,003,200 feet.

Step-by-step solution

Write down the given distance in miles

The distance between Boston and New York City is given as 190 miles.

Convert miles to kilometers

To convert miles to kilometers, multiply the number of miles by the conversion factor 1.60934. \(190 \text{miles} \times 1.60934 \frac{\text{kilometers}}{\text{mile}} = 305.7756 \text{kilometers}\) So, the distance between Boston and New York City is approximately 305.78 kilometers.

Convert kilometers to meters

We already have the distance in kilometers, so now we just need to convert it to meters. To do this, multiply the number of kilometers by the conversion factor 1000. \(305.7756 \text{kilometers} \times 1000 \frac{\text{meters}}{\text{kilometer}} = 305775.6 \text{meters}\) So, the distance between Boston and New York City is approximately 305,776 meters.

Convert miles to feet

Finally, let's convert the given distance in miles to feet. To do this, multiply the number of miles by the conversion factor 5280. \(190 \text{miles} \times 5280 \frac{\text{feet}}{\text{mile}} = 1003200 \text{feet}\) So, the distance between Boston and New York City is approximately 1,003,200 feet. After we have completed the conversion, we get the following results: - 305.78 kilometers - 305,776 meters - 1,003,200 feet

Key concepts

Miles to Kilometers Conversion

Converting miles to kilometers is a common requirement in understanding distances. If you're unfamiliar with the metric system, this might initially seem a bit tricky, but it's actually quite straightforward. The essential factor to remember is the conversion factor: one mile equals approximately 1.60934 kilometers.

This conversion factor enables you to translate any given distance in miles to kilometers easily. For instance, if you have a distance of 190 miles, you apply this conversion factor by multiplying the number of miles by 1.60934. Thus, the calculation is:

• \(190 \times 1.60934 = 305.7756\) kilometers

Remember to pay attention to significant figures, especially if you're required to give your answer to a certain number of decimal places. In this particular case, rounding to two decimal places gives us approximately 305.78 kilometers.

So, through this simple multiplication, you can convert miles to kilometers, which comes in handy for homework exercises and everyday situations.

Measurement Conversion Factors

Conversion factors play a vital role in converting measurements between different units. But what exactly are they? In simple terms, a conversion factor is a number used to change one unit of measurement to another. These factors rely on established equivalencies between metrics.

For distance, these might include:

• 1 mile = 1.60934 kilometers
• 1 kilometer = 1000 meters
• 1 mile = 5280 feet

To use a conversion factor, you multiply the given value by the conversion factor. This scales your measurement up or down based on the relationship established between the units.

Why are conversion factors so important? They ensure uniformity and accuracy when switching between units. Understanding these factors allows you to seamlessly interpret or convert measurements across different systems, be it for school tasks or finding your way around a new country with different metrics.

Conversion Between Units of Distance

Switching between units of distance is a fundamental skill when dealing with measurements, especially as different countries use different systems. It’s essential to understand how to translate distances from one unit to another effectively.

In our example of converting the distance between Boston and New York City, we've learned about translating from miles to kilometers, meters, and feet. Each of these conversions involves identifying the right measurement unit and applying the correct conversion factor.

For instance, converting kilometers to meters simply requires multiplying by 1000, as there are exactly 1000 meters in a kilometer. On the other hand, converting miles directly to feet requires a different conversion factor, specifically 5280 feet per mile.

These conversions highlight that:

• Using consistent conversion factors allows for seamless transitions between units.
• Knowing how these factors relate allows for swift problem-solving.
• Practicing these conversions builds confidence in handling various unit scenarios.

Mastering conversions between units of distance not only helps with school exercises but also equips you with a practical tool for international travel and scientific work.