How to Divide Numbers in Scientific Notation: Step-by-Step Guide
Quick Answer
To divide numbers in scientific notation, divide the coefficients and subtract the exponents. For instance, dividing 4.8 x 10^0 by 7.65 x 10^5 results in approximately 6.27 x 10^-6.
Dividing numbers in scientific notation can seem tricky at first, but once you understand the basic principles, it becomes much easier. Let’s break it down step by step using the example of dividing 4.8 x 10^0 by 7.65 x 10^5.
### Step 1: Understand the Power of Zero
Before starting the division, it’s essential to clarify what happens when a number is raised to the power of zero. Remember, any non-zero number raised to the power of zero equals one. Thus, we have:
- **10^0 = 1**
This means our numerator simplifies to:
- **4.8 x 10^0 = 4.8 x 1 = 4.8**
### Step 2: Rewrite the Fraction
Now, we can rewrite our fraction as:
\[
\frac{4.8}{7.65 \times 10^5}
\]
### Step 3: Separate the Coefficients and Powers of Ten
In scientific notation, we can treat the numbers separately. We can express our division as:
\[
\frac{4.8}{7.65} \times \frac{1}{10^5}
\]
Here, we start by dividing 4.8 by 7.65:
- **4.8 ÷ 7.65 ≈ 0.627**
### Step 4: Simplify the Power of Ten
Next, we need to handle the powers of ten. Since we have 1 (from 10^0) divided by 10^5, we can express this as:
\[
\frac{1}{10^5} = 10^{-5}
\]
### Step 5: Combine the Results
Putting it all together, we have:
\[
0.627 \times 10^{-5}
\]
### Step 6: Convert to Proper Scientific Notation
Scientific notation requires that the coefficient be between 1 and 10. To convert 0.627 into proper scientific notation, we can write it as:
\[
6.27 \times 10^{-1}
\]
Now we multiply this by \(10^{-5}\):
\[
6.27 \times 10^{-1} \times 10^{-5} = 6.27 \times 10^{-6}
\]
### Conclusion
Therefore, when you divide 4.8 x 10^0 by 7.65 x 10^5, the final answer in scientific notation is approximately:
\[6.27 \times 10^{-6}\]
Understanding how to manipulate the coefficients and the powers of ten will allow you to tackle other problems in scientific notation with confidence. Practice with different numbers to strengthen your skills further. This method is not only applicable in mathematics but also in fields like physics and engineering, where scientific notation is frequently used to handle very large or small numbers efficiently.
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