What is the quantity 13.5 gigameters expressed in decimal notation with standard units?
The correct answer and explanation is:
Correct Answer:
13.5 gigameters = 13,500,000,000 meters
Explanation (300 words):
To express 13.5 gigameters (Gm) in decimal notation with standard units, we need to understand the metric prefix “giga-“.
Step 1: Understand the Prefix
In the metric system:
- 1 gigameter (Gm) = 1,000,000,000 meters (m)
This is equal to 10910^9 meters.
Step 2: Multiply the Value
Given the quantity is 13.5 Gm, multiply by the value of one gigameter in meters: 13.5×1,000,000,000=13,500,000,000 meters13.5 \times 1,000,000,000 = 13,500,000,000 \text{ meters}
So, 13.5 gigameters = 13,500,000,000 meters in decimal notation.
Why This Matters
Using scientific or decimal notation helps in scientific communication. The International System of Units (SI) uses prefixes like giga-, mega-, kilo-, etc., to make very large or small measurements easier to express. However, for detailed calculation or when exact numerical values are needed (like in engineering or astronomy), converting to standard units (meters in this case) is essential.
Decimal Notation vs Scientific Notation
Decimal notation means writing the number in its full numeric form:
- Decimal: 13,500,000,000
- Scientific: 1.35×10101.35 \times 10^{10}
While scientific notation is compact, decimal notation is preferred in some contexts where exact place values are necessary, such as accounting or certain types of measurement displays.
Conclusion
13.5 gigameters, when expressed in decimal notation with standard SI units, becomes 13,500,000,000 meters. Understanding how to convert metric prefixes is crucial in science, engineering, and technology.