Absolutely! Let’s perform the operations using the provided numbers in scientific notation.
Here are the numbers we will work with:
- \( 3.2 \times 10^4 \)
- \( 1.95 \times 10^6 \)
- \( 8.03 \times 10^{-8} \)
- \( 2.56 \times 10^{-2} \)
- \( 4.82 \times 10^{12} \)
1. Addition
Let's add \( 3.2 \times 10^4 \) and \( 1.95 \times 10^6 \):
To add numbers in scientific notation, they must have the same exponent.
- Convert \( 3.2 \times 10^4 \) to have an exponent of \( 10^6 \): \[ 3.2 \times 10^4 = 0.032 \times 10^6 \]
Now we can add: \[ 0.032 \times 10^6 + 1.95 \times 10^6 = (0.032 + 1.95) \times 10^6 = 1.982 \times 10^6 \]
2. Subtraction
Now let's subtract \( 2.56 \times 10^{-2} \) from \( 8.03 \times 10^{-8} \):
Again, we need to convert these to the same exponent:
- Convert \( 8.03 \times 10^{-8} \) to have an exponent of \( 10^{-2} \): \[ 8.03 \times 10^{-8} = 0.0000803 \times 10^{-2} \]
So now we can subtract: \[ 0.0000803 \times 10^{-2} - 2.56 \times 10^{-2} = (0.0000803 - 2.56) \times 10^{-2} = -2.5599197 \times 10^{-2} \]
3. Multiplication
Now let’s multiply \( 4.82 \times 10^{12} \) by \( 1.95 \times 10^6 \):
We multiply the coefficients and add the exponents: \[ 4.82 \times 1.95 = 9.399 \] \[ 10^{12} \times 10^6 = 10^{12 + 6} = 10^{18} \]
So the product is: \[ 9.399 \times 10^{18} \]
4. Division
Finally, let's divide \( 1.95 \times 10^6 \) by \( 8.03 \times 10^{-8} \):
We divide the coefficients and subtract the exponents: \[ \frac{1.95}{8.03} \approx 0.2435 \] \[ 10^{6} \div 10^{-8} = 10^{6 - (-8)} = 10^{6 + 8} = 10^{14} \]
So the quotient is: \[ 0.2435 \times 10^{14} = 2.435 \times 10^{13} \quad (\text{after adjusting the coefficient}) \]
Summary of Operations:
- Addition: \( 1.982 \times 10^6 \)
- Subtraction: \( -2.5599197 \times 10^{-2} \)
- Multiplication: \( 9.399 \times 10^{18} \)
- Division: \( 2.435 \times 10^{13} \)
If you have any more questions or need more calculations, feel free to ask!
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