What is the product of 1000×10000?
The Correct Answer and Explanation is :
The product of (1000) and (10000) is (10,000,000) (or (10^7) in scientific notation).
Explanation:
To understand how to arrive at this product, we can break down the multiplication into simpler parts:
- Understanding the Numbers:
- (1000) can be expressed as (10^3) because (1000) is equivalent to (10) multiplied by itself three times: (10 \times 10 \times 10).
- (10000) is (10^4), representing (10) multiplied by itself four times: (10 \times 10 \times 10 \times 10).
- Applying the Laws of Exponents:
When multiplying numbers with the same base, we add the exponents:
[
10^3 \times 10^4 = 10^{3+4} = 10^7.
]
This means that (1000 \times 10000) can be simplified to (10^7). - Converting Back to Standard Form:
The scientific notation (10^7) equals (10,000,000) in standard numerical form. This is achieved by placing a (1) followed by (7) zeros. - Real-world Context:
Understanding large numbers is essential in various fields, such as finance, data science, and statistics. For example, a population of (10,000,000) could refer to a large city or country, or it could represent sales figures for a company in a particular year. - Importance of Multiplication:
Multiplication is a fundamental arithmetic operation that allows us to calculate large numbers quickly. It’s not only useful in academic settings but also vital in real-life applications like budgeting, resource allocation, and analyzing data.
In conclusion, the multiplication of (1000) and (10000) yielding (10,000,000) highlights the power of numbers and the efficiency of multiplication in managing large quantities.