Question

Convert the following metric measures by moving the decimal. $2\mathrm{kL}=$ ______ $\mathrm{L}$

Short answer

2 kL = 2000 L

Step-by-step solution

Understand the Prefix kilo- (k)

The prefix "kilo-" is a metric system prefix that means 1000. Therefore, 1 kiloliter (kL) is equal to 1000 liters (L).

Apply the Conversion

Since 1 kL equals 1000 L, to convert 2 kL to liters, you need to multiply 2 by 1000.

Perform the Multiplication

Calculate the number of liters by multiplying 2 by 1000: $$2\times 1000=2000\text{ L}$$

Move the Decimal

To convert from kiloliters to liters, you can simply move the decimal point three places to the right (because kilo- means 1000, or ${10}^3$). Start from 2.000 (2 kL) and move the decimal three places right, yielding 2000.

Key concepts

Metric System

The metric system is a standardized system of measurement used worldwide. It's especially common in scientific and international contexts. This system is based on multiples of ten, making conversions straightforward and logical. For instance, all units are related by powers of ten, allowing for easy conversion by simply moving the decimal point.

Some of the basic units include the meter for length, the liter for volume, and the gram for weight. To convert between these units, you just need to understand their prefixes, which indicate multiples or fractions of the base unit. This system thrives on simplicity, which is one reason it's favored globally.

Decimal Movement

The concept of decimal movement is a handy technique in metric conversions. Because the metric system is based on powers of ten, conversions are made by moving the decimal point.

For example, when converting from a larger unit like kiloliters (kL) to a smaller unit like liters (L), you move the decimal point to the right. The number of places moved corresponds to the power of ten involved in the prefix. Conversely, moving from a smaller unit to a larger unit requires moving the decimal point to the left.

• Moving the decimal right: Larger to smaller (e.g., kL to L)
• Moving the decimal left: Smaller to larger (e.g., L to kL)

This technique capitalizes on the base-10 nature of the metric system, making conversions quick and less prone to error.

Metric Prefixes

Metric prefixes are critical components of the metric system. They provide precise information about the size of the units. Each prefix represents a specific power of ten:

• Kilo- (k) means 1000 or ${10}^3$
• Milli- (m) means one-thousandth or ${10}^{-3}$
• Centi- (c) means one-hundredth or ${10}^{-2}$

These prefixes help in scaling units up or down without changing the base units.

For instance, knowing that "kilo-" indicates 1000 times the base unit (as with a kiloliter being 1000 liters) makes large and small units easy to comprehend and convert. These prefixes are uniform across all metric units, whether you're dealing with lengths, areas, volumes, or masses.

Volume Conversion

Converting volume measurements in the metric system requires understanding the prefixes and the rule of decimal movement. When working with volumes like liters, it’s crucial to grasp both the numerical part and the unit part of the measurement to perform effective conversions.

Let's say you have a quantity in kiloliters and you want to find out how many liters it represents. You know that each kiloliter is equal to 1000 liters. So, multiplying the number of kiloliters by 1000 gives you the equivalent in liters, as shown by the equation:$$2\text{ kL}=2\times 1000=2000\text{ L}$$Alternatively, applying decimal movement can simplify this further by moving the decimal point three places to the right, as this correlates with the kilo- prefix meaning ${10}^3$.

These steps maintain consistency and ease in converting all metric volume measures effectively.