Question

What does the prefix kilo (k) mean? How can this prefix be used to modify the description of an obstacle course that is \(1450 \mathrm{~m}\) long?

Short answer

The prefix 'kilo' means 1000. 1450 meters is 1.45 kilometers.

Step-by-step solution

Understanding the Prefix

The prefix 'kilo' is derived from the Greek word 'chilioi', meaning one thousand. In the metric system, the prefix 'kilo' signifies a factor of one thousand (1000). This means when you see 'kilo' in front of any unit, it is multiplied by 1000.

Identifying the Unit

The unit we are dealing with in this question is meters, as the obstacle course is measured in meters. The unit associated with the prefix 'kilo' in the metric system is 'kilometers' (km), which means one kilometer is equal to 1000 meters.

Converting Meters to Kilometers

To convert meters into kilometers, we need to divide the number of meters by 1000, since one kilometer is equal to 1000 meters. For the given obstacle course length, we have 1450 meters.

Performing the Conversion

Using the conversion formula: \[\text{kilometers} = \frac{\text{meters}}{1000}\]we calculate: \[\text{kilometers} = \frac{1450}{1000} = 1.45\]So, the obstacle course is 1.45 kilometers long.

Key concepts

Kilo Prefix

The prefix "kilo" is a common term in the metric system, representing a multiplier of one thousand. This prefix originates from the Greek word "chilioi," which translates to "one thousand." Therefore, whenever you see the prefix "kilo," you should understand that the value is 1000 times the base unit.
This concept is essential as it allows for concise representation of large quantities. For example, instead of saying "1000 meters," you can simply say "1 kilometer." This makes communication more efficient and easier to understand.

• The letter "k" represents the kilo prefix
• 1 kilogram equals 1000 grams
• 1 kiloliter equals 1000 liters

Metric Conversions

Metric conversions are processes of converting one unit of measurement into another, using established conversion factors. The metric system is particularly convenient because it is a decimal-based system, meaning it uses powers of ten. This simplifies calculations significantly.
Conversion between metric units can be done by either multiplying or dividing by factors like 10, 100, or 1000. The critical part is understanding the relationship between the units. Whether you're converting grams to kilograms, meters to kilometers, or any other metric units, the rule remains the same: know your conversion factor and either multiply or divide accordingly.

• Identify the units you are converting between
• Use the correct multiplication or division factor
• Double-check your calculations

Kilometers to Meters Conversion

The conversion from kilometers to meters involves a simple process, thanks to the metric system's design. Since the prefix "kilo" means 1000, converting kilometers to meters is straightforward: you multiply the number of kilometers by 1000.
Conversely, if you are converting meters into kilometers, you divide by 1000. This is because one kilometer is defined as 1000 meters. In the given exercise, converting 1450 meters into kilometers involves the formula:
\[ \text{kilometers} = \frac{\text{meters}}{1000} \]
With 1450 meters, the calculation becomes: \( \frac{1450}{1000} = 1.45 \) kilometers.

• Conversion factor from kilometers to meters: Multiply by 1000
• Conversion factor from meters to kilometers: Divide by 1000
• Always use the given formula to ensure accurate conversion