Practice adding, subtracting, multiplying, and dividing numbers written in scientific notation for each part use the following numbers/ 3.2*10^4 1.95*10^6

Answer 1

Sure! Let’s practice adding, subtracting, multiplying, and dividing the numbers \( 3.2 \times 10^4 \) and \( 1.95 \times 10^6 \).

1. Addition:

To add numbers in scientific notation, they must have the same exponent. We can rewrite \( 3.2 \times 10^4 \) to have the same exponent as \( 1.95 \times 10^6 \):

\[ 3.2 \times 10^4 = 0.032 \times 10^6 \]

Now we can add them:

\[ 0.032 \times 10^6 + 1.95 \times 10^6 = (0.032 + 1.95) \times 10^6 = 1.982 \times 10^6 \]

2. Subtraction:

We can use the same adjustment for subtraction:

\[ 0.032 \times 10^6 - 1.95 \times 10^6 = (0.032 - 1.95) \times 10^6 = -1.918 \times 10^6 \]

3. Multiplication:

For multiplication, we multiply the coefficients and add the exponents:

\[ (3.2 \times 10^4) \times (1.95 \times 10^6) = (3.2 \times 1.95) \times (10^4 \times 10^6) \] \[ = 6.24 \times 10^{4 + 6} = 6.24 \times 10^{10} \]

4. Division:

For division, we divide the coefficients and subtract the exponents:

\[ \frac{3.2 \times 10^4}{1.95 \times 10^6} = \left(\frac{3.2}{1.95}\right) \times \left(10^{4 - 6}\right) \] \[ = 1.641 \times 10^{-2} \quad (\text{approximately}) \]

Summary of Results:

1. Addition: \( 1.982 \times 10^6 \)
2. Subtraction: \( -1.918 \times 10^6 \)
3. Multiplication: \( 6.24 \times 10^{10} \)
4. Division: \( 1.641 \times 10^{-2} \) (approximately)

Answer 2

Simplify it and just show the work you used to come to this answer

Answer 3

Certainly! Here’s the simplified work for each operation, step by step:

1. Addition:

• Convert \( 3.2 \times 10^4 \) to the same exponent as \( 1.95 \times 10^6 \): \[ 3.2 \times 10^4 = 0.032 \times 10^6 \]
• Now 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:

• Using the same conversion: \[ 0.032 \times 10^6 - 1.95 \times 10^6 = (0.032 - 1.95) \times 10^6 = -1.918 \times 10^6 \]

3. Multiplication:

• Multiply the coefficients and add the exponents: \[ (3.2 \times 10^4) \times (1.95 \times 10^6) = (3.2 \times 1.95) \times (10^{4 + 6}) \] \[ = 6.24 \times 10^{10} \]

4. Division:

• Divide the coefficients and subtract the exponents: \[ \frac{3.2 \times 10^4}{1.95 \times 10^6} = \left(\frac{3.2}{1.95}\right) \times \left(10^{4 - 6}\right) \] \[ = 1.641 \times 10^{-2} \quad (\text{approximately}) \]

Final Results:

1. Addition: \( 1.982 \times 10^6 \)
2. Subtraction: \( -1.918 \times 10^6 \)
3. Multiplication: \( 6.24 \times 10^{10} \)
4. Division: \( 1.641 \times 10^{-2} \) (approximately)

Answer 4

What does /frac mean?

Answer 5

The command /frac is a common notation used in typesetting to create a fraction. In LaTeX, which is a typesetting system often used for mathematical and scientific documents, the command \frac{numerator}{denominator} is used to display fractions in a clear format.

For example:

• If you want to represent the fraction \( \frac{a}{b} \), you would write \frac{a}{b} in LaTeX.

In plain text, it usually just means to denote division or a fractional relationship, such as writing \( \frac{3.2}{1.95} \) to indicate that 3.2 is divided by 1.95.

If you're asking about a specific context where you've seen /frac, please let me know, and I can provide more tailored information!