Convert 4.5 x 104 to decimal format.
The Correct Answer and Explanation is:
Correct Answer:
4.5 × 10⁴ = 45,000
Explanation:
Scientific notation is a compact way of expressing very large or very small numbers. The number 4.5 × 10⁴ means the decimal point in 4.5 needs to be moved four places to the right, because the exponent on the base 10 is positive 4.
To understand this, begin with the number 4.5. Multiplying by 10⁴ is the same as multiplying by 10,000. That operation increases the size of the number by shifting the decimal:
- Start: 4.5
- Move 1 place → 45
- Move 2 places → 450
- Move 3 places → 4,500
- Move 4 places → 45,000
Adding the necessary zeros completes the transformation.
In scientific notation, the base 10 tells how many times the decimal should be moved:
- Positive exponent → move the decimal to the right
- Negative exponent → move the decimal to the left
This notation is especially useful in science and engineering to represent values like distances in space, atomic sizes, or data storage capacity.
In this case, 4.5 × 10⁴ helps simplify the visual handling of 45,000, which might otherwise appear cluttered with trailing zeros. After conversion, the number becomes clearer in a real-world context, such as 45,000 people, 45,000 kilometers, or 45,000 grams.
By translating scientific notation into standard form, calculations, estimations, and comparisons become more intuitive, especially when dealing with practical applications or data presentation.
