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Chapter 1: Problem 46

Fill in each blank. \(1 \mathrm{~kL}=\)_______ L

Short Answer

Expert verified
1 kL = 1,000 L

Step by step solution

01

Understand the Metric System

The metric system is based on powers of 10. 'Kilo' in kL stands for 1,000 times the base unit. Therefore, 1 kL (kiloliter) means 1,000 liters.
02

Conversion from kL to L

To convert kiloliters to liters, multiply by 1,000. So, 1 kL = 1,000 * 1 L.
03

Fill in the Blank

Place the result of the conversion into the blank space. Thus, 1 kL = 1,000 L.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Metric System
The metric system is an international system of measurement that is used in almost every country worldwide. It is a decimal-based system, meaning that it is based on powers of ten. This system makes calculations straightforward and conversion easy, as each unit changes by a factor of ten. Units in the metric system include meters for length, liters for volume, and grams for mass.
A key feature of the metric system is the use of prefixes to indicate multiples of ten. For example:
  • "milli" means one-thousandth (0.001)
  • "centi" means one-hundredth (0.01)
  • "deci" means one-tenth (0.1)
  • "deka" means ten (10)
  • "hecto" means one hundred (100)
  • "kilo" means one thousand (1,000)
These prefixes make it simple to move between different scales of measurement, simply by multiplying or dividing by powers of ten.
Kiloliter to Liter Conversion
Converting kiloliters (kL) to liters (L) is a straightforward process thanks to the decimal-based nature of the metric system. Since "kilo" denotes 1,000 times the base unit, a kiloliter is inherently 1,000 liters. Therefore, to convert kiloliters to liters, you just multiply by 1,000.
  • For example, 1 kL equals 1,000 L because 1 kL = 1 脳 1,000 L = 1,000 L.
  • If you have 2 kL, the conversion to liters involves multiplying by 1,000, resulting in 2,000 L.
  • Similarly, 0.5 kL would convert to 500 L, as 0.5 脳 1,000 L = 500 L.
This method applies to all metric conversions, making it easy to convert units by simply adjusting by the appropriate power of ten.
The Role of Powers of Ten in Conversions
Powers of ten are fundamental in the metric system and are the reason behind its simplicity. Every conversion between metric units is just a matter of moving the decimal point, thanks to these powers.
When you see a prefix like "kilo," what it actually represents is a multiplication by 10 raised to the power of 3 (\(10^3\)). So, 1 kiloliter (kL) is 1 脳 10^3 or 1,000 liters.
This concept can be extended to any metric conversion:
  • To move from a smaller unit to a larger one (like from liters to kiloliters), you divide by a power of ten (1,000 in this case).
  • To move from a larger unit to a smaller one, you multiply by a power of ten.
This unified approach not only simplifies the math but also reinforces the idea that the metric system is both dependable and logically structured.

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