Sure! Let's go through the operations step by step.
a. Addition
Let's add \( 3.2 \times 10^4 \) and \( 2.56 \times 10^{-2} \).
To add these, we first need to make sure the exponents are the same:
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Convert \( 3.2 \times 10^4 \):
- \( 3.2 \times 10^4 = 32,000 \).
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Convert \( 2.56 \times 10^{-2} \):
- \( 2.56 \times 10^{-2} = 0.0256 \).
Now we can add the two numbers: \[ 32,000 + 0.0256 = 32,000.0256 \]
Now let's convert \( 32,000.0256 \) back to scientific notation.
- It’s \( 3.200000256 \times 10^4 \) which we can approximate to: \[ \mathbf{3.20 \times 10^4} \]
b. Subtraction
Now let's subtract \( 4.82 \times 10^{12} \) from \( 1.95 \times 10^{6} \).
Again, we will use the same exponent for comparison:
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Convert \( 4.82 \times 10^{12} \):
- Consider \( 4.82 \times 10^{12} = 4,820,000,000,000 \).
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Convert \( 1.95 \times 10^{6} \):
- \( 1.95 \times 10^{6} = 1,950,000 \).
Now we can subtract: \[ 1,950,000 - 4,820,000,000,000 = -4,818,050,000,000 \]
To convert \( -4,818,050,000,000 \) back to scientific notation:
- It’s written as: \[ \mathbf{-4.81805 \times 10^{12}} \]
So, the results are:
- a. \( 3.20 \times 10^4 \)
- b. \( -4.81805 \times 10^{12} \)