How do you convert 8.5×10-2 to standard form
The Correct Answer and Explanation is:
To convert (8.5 \times 10^{-2}) to standard form, we need to understand how scientific notation works and how to manipulate the exponent of 10 to express the number in the proper format.
Step-by-Step Explanation:
- Understanding Scientific Notation:
Scientific notation is a way of expressing very large or very small numbers in the form:
[
a \times 10^n
]
where:
- (a) is a number between 1 and 10 (or greater than or equal to 1 but less than 10).
- (n) is an integer (positive or negative) that tells us how many places the decimal point should move.
- Analyzing (8.5 \times 10^{-2}):
- The coefficient, (8.5), is already between 1 and 10, so we do not need to adjust it.
- The exponent is (-2), indicating that the decimal point in (8.5) should move two places to the left.
- Moving the Decimal Point:
To apply the exponent of (-2), move the decimal point in (8.5) two places to the left:
- Starting with (8.5), moving one place to the left gives us (0.85).
- Moving the decimal point one more place to the left gives us (0.085).
- Final Result:
After moving the decimal point two places to the left, we get:
[
8.5 \times 10^{-2} = 0.085
]
This is the number in standard decimal form.
Conclusion:
The expression (8.5 \times 10^{-2}) in standard form (or decimal notation) is (0.085). Scientific notation is particularly useful in representing numbers that are either very large or very small, and converting between scientific notation and standard form involves shifting the decimal point according to the exponent. A positive exponent moves the decimal to the right, while a negative exponent moves it to the left.