Final answer:
The prefix for the power of ten represented by 10^3 is 'kilo-', which indicates a multiplication factor of one thousand. Understanding integer powers and their corresponding prefixes is crucial in scientific notation, which is used to express large and small numbers conveniently.
Step-by-step explanation:
The prefix that defines the power of ten for 10^3 is 'kilo-'. This prefix signifies a multiplication factor of one thousand, which we can see clearly by understanding that 10^3 equals 10 multiplied by itself three times, resulting in 1,000. It's essential to grasp the concept of integer powers to comprehend how to work with these prefixes effectively.
For instance, 10^3 is 10 · 10 · 10, which equals 1,000, without a doubt. This basic understanding is the foundation for working with scientific notation, where exponents of 10 indicate how many places the decimal point moves to convert a number into a digit number, simplifying the expression of very large or very small numbers.
When using scientific measurements, it is crucial to recognize the appropriate prefix corresponding to different powers of 10. As noted, kilo- is commonly used, and its symbol 'k' signifies a factor of 10^3. Other commonly used prefixes include mega- (M for 10^6) and milli- (m for 10^-3), where uppercase letters represent exponents greater than one and lowercase letters represent those less than one. Knowing these prefixes helps in converting and understanding measurements in the sciences and mathematics.