Question

Adding using Scientific Notation
1. (3.2 × 10^4) + (1.95 × 10^5)

Answer 1

To add the numbers in scientific notation, we first need to express them with the same exponent. Here are the steps:

1. **Convert (3.2 × 10^4) to the same exponent as (1.95 × 10^5)**:
\[
3.2 \times 10^4 = 3.2 \times 10^4 \times \frac{10^1}{10^1} = 3.2 \times 10^5 \div 10 = 0.32 \times 10^5
\]

2. **Now we can add (0.32 × 10^5) + (1.95 × 10^5)**:
\[
(0.32 + 1.95) \times 10^5 = 2.27 \times 10^5
\]

So, the final result is:
\[
(3.2 × 10^4) + (1.95 × 10^5) = 2.27 \times 10^5
\]

Answer 2

Subtraction using Scientific Notation
(2.56 × 10 ^- 2) - (4.82 × 10^ 12)

Answer 3

To perform the subtraction of the numbers in scientific notation \((2.56 × 10^{-2}) - (4.82 × 10^{12})\), we first need to express both numbers with the same exponent.

1. **Convert \(2.56 × 10^{-2}\) to the same exponent as \(4.82 × 10^{12}\)**:

Since \(10^{-2}\) is much smaller than \(10^{12}\), we can rewrite \(2.56 × 10^{-2}\) with an exponent of \(10^{12}\).

\[
2.56 × 10^{-2} = 2.56 × 10^{-2} × \frac{10^{14}}{10^{14}} = 0.0000256 × 10^{12}
\]

Thus,
\[
2.56 × 10^{-2} = 0.0000256 × 10^{12}
\]

2. **Now we can subtract**:
\[
(0.0000256 × 10^{12}) - (4.82 × 10^{12})
\]

We proceed to subtract the coefficients:
\[
(0.0000256 - 4.82) × 10^{12} ≈ -4.8199744 × 10^{12}
\]

3. **Final result**:

Since \(4.82\) is significantly larger than \(0.0000256\), this will give us a negative result. Therefore,
\[
(2.56 × 10^{-2}) - (4.82 × 10^{12}) = -4.8199744 × 10^{12}
\]

We can round this to suitable precision:
\[
\approx -4.82 × 10^{12}
\]

So the final answer is:
\[
(2.56 × 10^{-2}) - (4.82 × 10^{12}) \approx -4.82 × 10^{12}
\]

Answer 4

Just write the answer normally, what the heck does approx even mean???

Answer 5

My apologies for any confusion! The precise answer without approximation is:

\[
(2.56 × 10^{-2}) - (4.82 × 10^{12}) = -4.8199744 × 10^{12}
\]

If we want it in a more standard form:
\[
= -4.82 × 10^{12}
\]

Thank you for your understanding!

Answer 6

Multiplying using Scientific Notation
(8.03 × 10^ -8) x (2.56 × 10 ^-2)

Answer 7

To multiply numbers in scientific notation, you multiply the coefficients and add the exponents. Here are the steps for \((8.03 × 10^{-8}) × (2.56 × 10^{-2})\):

1. **Multiply the coefficients**:
\[
8.03 × 2.56 = 20.5588
\]

2. **Add the exponents**:
\[
(-8) + (-2) = -10
\]

3. **Combine the results**:
\[
20.5588 × 10^{-10}
\]

4. **Convert to proper scientific notation**:
The coefficient \(20.5588\) can be expressed as \(2.055588 × 10^{1}\), so:
\[
20.5588 × 10^{-10} = 2.055588 × 10^{1} × 10^{-10} = 2.055588 × 10^{-9}
\]

Thus, the final answer is:
\[
(8.03 × 10^{-8}) × (2.56 × 10^{-2}) = 2.055588 × 10^{-9}
\]

If rounded to three significant figures, it would be:
\[
= 2.06 × 10^{-9}
\]

Answer 8

Division using Scientific Notation
3.2 × 10^4
4.82 × 10 ^ 12

Answer 9

To divide numbers in scientific notation, you divide the coefficients and subtract the exponents. Here’s how you can divide \( (3.2 × 10^{4}) \) by \( (4.82 × 10^{12}) \):

1. **Divide the coefficients**:
\[
\frac{3.2}{4.82} \approx 0.6635
\]

2. **Subtract the exponents**:
\[
4 - 12 = -8
\]

3. **Combine the results**:
\[
0.6635 × 10^{-8}
\]

4. **Convert to proper scientific notation**:
To express \(0.6635\) in scientific notation, we can write it as \(6.635 × 10^{-1}\):
\[
0.6635 × 10^{-8} = 6.635 × 10^{-1} × 10^{-8} = 6.635 × 10^{-9}
\]

Thus, the final answer is:
\[
\frac{3.2 × 10^{4}}{4.82 × 10^{12}} = 6.635 × 10^{-9}
\]

If rounded to three significant figures, it would be:
\[
= 6.64 × 10^{-9}
\]