When 560,000 is written in scientific notation, what is the power of 10
The Correct Answer and Explanation is:
To express 560,000 in scientific notation, we need to follow these steps:
Step 1: Understanding Scientific Notation
Scientific notation is a way to express large or small numbers in the form of:a×10na \times 10^na×10n
where:
- a is a number greater than or equal to 1 but less than 10,
- n is an integer (the power of 10).
Step 2: Converting 560,000 to Scientific Notation
We start by moving the decimal point in 560,000 so that it is between the first two digits (5 and 6). This means we move the decimal point 5 places to the left:560,000=5.6×105560,000 = 5.6 \times 10^5560,000=5.6×105
Step 3: Understanding the Power of 10
The number of places we move the decimal point determines the power of 10:
- Since we moved the decimal point 5 places to the left, the power of 10 is 5.
Thus, when 560,000 is written in scientific notation, the power of 10 is 5.
Step 4: Why Use Scientific Notation?
Scientific notation helps simplify the handling of very large or very small numbers. By writing numbers in this way, it becomes easier to perform operations like multiplication or division, especially when dealing with very high or very low values. For example, instead of writing 560,000 each time, we can use 5.6 × 10⁵, which is more manageable in calculations.
Conclusion
So, when 560,000 is written in scientific notation, it is expressed as 5.6 × 10⁵, where the power of 10 is 5. This is because we move the decimal point 5 places to the left, making the power of 10 equal to 5.
