To solve the expression \(10 \times 0.00025 / (1.6 \times 10^{-8})\), we can break it down into manageable steps. This will not only help you find the answer but also give you a solid understanding of how to approach similar problems in the future. Let's go through it step by step.
Step 1: Simplifying the Multiplication
First, let's simplify the multiplication part of the expression. We have:
10 multiplied by 0.00025:
To make it easier, we can convert \(0.00025\) into scientific notation. It can be expressed as:
- 0.00025 = 2.5 \times 10^{-4}
Now, substituting this back into the expression gives us:
10 \times (2.5 \times 10^{-4})
Multiplying these together:
10 \times 2.5 = 25
So, we have:
25 \times 10^{-4}
In scientific notation, this can be expressed as:
2.5 \times 10^{-3} \quad (\text{since } 25 = 2.5 \times 10^1)
Step 2: Setting Up the Division
Now, we need to divide this result by \(1.6 \times 10^{-8}\):
Expression now looks like:
(2.5 \times 10^{-3}) / (1.6 \times 10^{-8})
Step 3: Dividing the Coefficients
Next, we divide the coefficients:
2.5 divided by 1.6:
Using a calculator or doing the math, we find:
2.5 / 1.6 = 1.5625
Step 4: Dividing the Powers of Ten
Now, we handle the powers of ten. When dividing, we subtract the exponents:
10^{-3} divided by 10^{-8}:
-3 - (-8) = -3 + 8 = 5
So, we have:
10^{5}
Step 5: Combining the Results
Now, we can combine the results from the coefficients and the powers of ten:
Final result:
1.5625 \times 10^{5}
Basic Rules for Similar Problems
When solving problems like this, keep these fundamental rules in mind:
- Scientific Notation: Always convert numbers into scientific notation for easier multiplication and division.
- Multiplication: Multiply the coefficients and add the exponents when dealing with powers of ten.
- Division: Divide the coefficients and subtract the exponents when dividing powers of ten.
- Order of Operations: Follow the order of operations (parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right).
By following these steps and rules, you'll be well-equipped to tackle similar problems in your studies of electricity and beyond. If you have any more questions or need further clarification, feel free to ask!
