Express the following number in scientific notation.
5,300,000
The Correct Answer and Explanation is:
To express the number 5,300,000 in scientific notation, we follow a systematic approach. Scientific notation is a method of writing numbers that are either very large or very small in a compact form, which makes them easier to read and work with. The format for scientific notation is:
[
a \times 10^n
]
where ( a ) is a number greater than or equal to 1 but less than 10, and ( n ) is an integer that represents the power of 10.
Step-by-Step Process
- Identify the Significant Digits:
For the number 5,300,000, we first identify the significant digits. The significant digits here are 5.3. This is done by looking at the first non-zero digit and retaining it along with any digits that follow it until we have one digit before the decimal point. - Determine the Exponent:
Next, we need to find the exponent ( n ). This is done by counting how many places we move the decimal point to the left to get from the original number (5,300,000) to our significant digits (5.3). The decimal point in 5,300,000 is implicitly at the end of the number, so when we move it left to place it after the 5, we move it 6 places:
- 5,300,000 → 530,000 → 53,000 → 5,300 → 530 → 53 → 5.3
- Construct the Scientific Notation:
After moving the decimal point, we note that we moved it 6 places to the left. Therefore, we can express 5,300,000 in scientific notation as:
[
5.3 \times 10^6
]
Conclusion
Thus, the final answer in scientific notation for the number 5,300,000 is:
[
\boxed{5.3 \times 10^6}
]
This format simplifies calculations and makes it easier to understand the magnitude of large numbers. In scientific contexts, this notation is especially useful in fields such as physics, chemistry, and engineering, where extremely large or small values are common.