Question

Express the quantity \(254,998 \mathrm{~m}\) in each unit. MISSED THIS? Read Section 1.6; Watch KCV 1.6 a. \(\mathrm{km}\) b. \(\mathrm{Mm}\) c. \(\mathrm{mm}\) d. \(\mathrm{cm}\)

Short answer

a. 254.998 km, b. 0.254998 Mm, c. 254,998,000 mm, d. 25,499,800 cm

Step-by-step solution

Convert to Kilometers

Since 1 kilometer equals 1000 meters, you divide the number of meters by 1000 to convert to kilometers. Calculate: \(\frac{254,998 \text{ m}}{1000} = 254.998 \text{ km}\).

Convert to Megameters

Given that 1 Megameter equals 1,000,000 meters, you divide the number of meters by 1,000,000 to convert to Megameters. Calculate: \(\frac{254,998 \text{ m}}{1,000,000} = 0.254998 \text{ Mm}\).

Convert to Millimeters

Since 1 meter equals 1000 millimeters, you multiply the number of meters by 1000 to convert to millimeters. Calculate: \(254,998 \text{ m} \times 1000 = 254,998,000 \text{ mm}\).

Convert to Centimeters

Knowing that 1 meter equals 100 centimeters, multiply the number of meters by 100 to convert to centimeters. Calculate: \(254,998 \text{ m} \times 100 = 25,499,800 \text{ cm}\).

Key concepts

Understanding Kilometers to Meters Conversion

Metric unit conversion is a crucial skill in understanding measurements, especially when dealing with varying scales. One common conversion is turning kilometers into meters. A kilometer (km), being larger than a meter (m), requires a straightforward calculation to convert it.

In the metric system, one kilometer is equivalent to 1,000 meters. To make the conversion, you simply need to multiply the number of kilometers by 1,000. For example, if you have 2 km, you will have 2,000 meters after conversion (\(2 \text{ km} \times 1000 = 2000 \text{ m}\)).

This process is easily scalable, which allows you to handle larger numbers without adding complexity. Whether you're converting small distances or covering longer stretches, knowing this basic conversion ratio makes these calculations accessible.

Megameters to Meters Simplified

When larger distances come into play, the unit of Megameters (Mm) might be used. While it's not as commonly referenced as kilometers or meters, understanding how to convert Megameters to meters is just as simple.

One Megameter is equal to one million meters (\(1 \text{ Mm} = 1,000,000 \text{ m}\)). To convert from Megameters to meters, multiply your figure in Megameters by one million. For instance, converting 3 Mm to meters would result in 3,000,000 meters (\(3 \text{ Mm} \times 1,000,000 = 3,000,000 \text{ m}\)).

This leap from smaller to enormously larger units can be daunting, but with the consistent decimal-based metric system, shifting between these units remains intuitive and versatile for various applications.

From Millimeters to Meters - A Small Scale Conversion

On the smaller end of the scale, millimeters to meters conversion is a common task in precision measurements. Millimeters (mm) are often used when exactness is required.

Since there are 1,000 millimeters in one meter (\(1 \text{ m} = 1000 \text{ mm}\)), converting mm to m involves dividing the number of millimeters by 1,000. For instance, if you're given 5000 mm, to find out how many meters this is, divide by 1000 (\(5000 \text{ mm} \text{ ÷ } 1000 = 5 \text{ m}\)).

This conversion is particularly useful in fields like engineering and manufacturing, where dimensions often need to be expressed in different scales to match various specifications and tolerances.

Converting Centimeters to Meters with Ease

Centimeters (cm) to meters (m) is likely the most frequently encountered conversion, especially in everyday scenarios such as measuring body height or lengths of objects.

Knowing that 100 centimeters make up 1 meter (\(1 \text{ m} = 100 \text{ cm}\)), the conversion process is simply a division by 100. To find the number of meters from a centimeter measurement, take the number of centimeters and divide by 100. For example, a measurement of 550 centimeters would translate to 5.5 meters (\(550 \text{ cm} \text{ ÷ } 100 = 5.5 \text{ m}\)).

This conversion remains straightforward and is vital for many activities, including construction, fabric measurement, or even while exercising or tracking growth charts in medicine.