. In this problem, you will practice adding, subtracting, multiplying, and dividing

Question

numbers written in scientific notation. For each part, use the following numbers. 3.2x10^4 1.95x10^6 8.03x10^-8 2.56 x 10^-2 4.82 x10^12

Answer 1

Let's perform the arithmetic operations (addition, subtraction, multiplication, and division) using the numbers in scientific notation you've provided. We'll use the following numbers:

• \( a = 3.2 \times 10^4 \)
• \( b = 1.95 \times 10^6 \)
• \( c = 8.03 \times 10^{-8} \)
• \( d = 2.56 \times 10^{-2} \)
• \( e = 4.82 \times 10^{12} \)

1. Addition

We can only add numbers with the same exponent. To add different orders of magnitude, we may need to convert them.

a + b: \[ 3.2 \times 10^4 + 1.95 \times 10^6 = 3.2 \times 10^4 + 195 \times 10^4 = (3.2 + 195) \times 10^4 = 198.2 \times 10^4 = 1.982 \times 10^6 \]

c + d: To add \( c \) and \( d \), we need matching exponents as well: \[ 8.03 \times 10^{-8} + 2.56 \times 10^{-2} = 8.03 \times 10^{-8} + 256 \times 10^{-8} = (8.03 + 256) \times 10^{-8} = 264.03 \times 10^{-8} = 2.6403 \times 10^{-6} \]

2. Subtraction

Again, we can only subtract numbers with the same exponent.

b - a: \[ 1.95 \times 10^6 - 3.2 \times 10^4 = 1.95 \times 10^6 - 0.032 \times 10^6 = (1.95 - 0.032) \times 10^6 = 1.918 \times 10^6 \]

d - c: \[ 2.56 \times 10^{-2} - 8.03 \times 10^{-8} \approx 2.56 \times 10^{-2} (\text{as } c \text{ is negligible}) \]

3. Multiplication

When multiplying numbers in scientific notation, you multiply the coefficients and add the exponents.

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

c \cdot d: \[ (8.03 \times 10^{-8})(2.56 \times 10^{-2}) = (8.03 \times 2.56) \times 10^{-8 - 2} = 20.5668 \times 10^{-10} = 2.05668 \times 10^{-9} \]

4. Division

When dividing numbers in scientific notation, you divide the coefficients and subtract the exponents.

b / a: \[ \frac{1.95 \times 10^6}{3.2 \times 10^4} = \left(\frac{1.95}{3.2}\right) \times 10^{6 - 4} = 0.609375 \times 10^2 = 6.09375 \times 10^{1} \]

e / d: \[ \frac{4.82 \times 10^{12}}{2.56 \times 10^{-2}} = \left(\frac{4.82}{2.56}\right) \times 10^{12 - (-2)} = 1.8828125 \times 10^{14} \]

Summary of Results

1. Addition:

   • \( a + b = 1.982 \times 10^6 \)
   • \( c + d = 2.6403 \times 10^{-6} \)

2. Subtraction:

   • \( b - a = 1.918 \times 10^6 \)
   • \( d - c \approx 2.56 \times 10^{-2} \)

3. Multiplication:

   • \( a \cdot b = 6.24 \times 10^{10} \)
   • \( c \cdot d = 2.05668 \times 10^{-9} \)

4. Division:

   • \( b/a = 6.09375 \times 10^1 \)
   • \( e/d = 1.8828125 \times 10^{14} \)

If you have any specific operation or further questions, feel free to ask!

Answer 2

Choose two of the scientific numbers from the list and add them. Show your
work

Answer 3

Let's choose two of the scientific numbers from the list and perform addition. We'll use:

• \( a = 3.2 \times 10^4 \)
• \( b = 1.95 \times 10^6 \)

Step 1: Align the Exponents

Before we can add these two numbers, we need to express them with the same exponent. We can choose to convert \( a \) to the same exponent as \( b \) (i.e., \( 10^6 \)).

Convert \( a \): \[ a = 3.2 \times 10^4 = 3.2 \times 10^4 \times \frac{100}{100} = 3.2 \times 10^{4} \times \frac{10^{2}}{10^{2}} = 3.2 \times 10^{6} \times 10^{-2} = 0.032 \times 10^{6} \]

Step 2: Add the Numbers

Now we can add \( 0.032 \times 10^6 \) to \( 1.95 \times 10^6 \):

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

Final Answer

Thus, the sum of \( 3.2 \times 10^4 \) and \( 1.95 \times 10^6 \) is: \[ 1.982 \times 10^6 \]

Answer 4

can you short it and make it look like a 8th grader

Answer 5

Sure! Here’s a simpler and shorter way to show the addition of the two scientific numbers:

Let's add:

• \( 3.2 \times 10^4 \)
• \( 1.95 \times 10^6 \)

Step 1: Change the Numbers to Have the Same Exponent

We will convert \( 3.2 \times 10^4 \) to have the same exponent as \( 1.95 \times 10^6 \).

Convert \( 3.2 \times 10^4 \): \[ 3.2 \times 10^4 = 3.2 \times 10^4 \times \frac{100}{100} = 0.032 \times 10^6 \]

Step 2: Add the Numbers

Now we add the two numbers: \[ 0.032 \times 10^6 + 1.95 \times 10^6 = (0.032 + 1.95) \times 10^6 = 1.982 \times 10^6 \]

Final Answer

So, the sum is: \[ 1.982 \times 10^6 \]

Answer 6

im confuses what dose the fraction have to do with it

Answer 7

I'm sorry for any confusion! The fraction was used to convert the number \(3.2 \times 10^4\) to the same exponent as \(1.95 \times 10^6\), but it may have made things more complicated than necessary.

Let’s simplify the explanation without using fractions:

Adding \(3.2 \times 10^4\) and \(1.95 \times 10^6\)

1. Convert \(3.2 \times 10^4\) to match the exponent of \(10^6\):

   Since \(10^4\) is much smaller than \(10^6\), we need to make it bigger. We can express \(10^4\) in terms of \(10^6\):

   \(3.2 \times 10^4 = 3.2 \times 10^4 \times 1\)

   To change it to \(10^6\), we remember that moving two places to the right means we divide the coefficient by \(100\). So: \[ 3.2 \times 10^4 = 0.032 \times 10^6 \]

2. Now, add the numbers:

   \[ 0.032 \times 10^6 + 1.95 \times 10^6 \] Combine the coefficients: \[ (0.032 + 1.95) \times 10^6 = 1.982 \times 10^6 \]

Final Answer

So, adding \(3.2 \times 10^4\) and \(1.95 \times 10^6\) gives us: \[ 1.982 \times 10^6 \]

I hope this explanation is clearer! Let me know if you have any more questions.

Answer 8

can you do it with out (( or #### or (/ pls

Answer 9

Of course! Let's keep it simple and straightforward without any extra symbols. Here’s how to add \(3.2 \times 10^4\) and \(1.95 \times 10^6\):

Step 1: Change the first number

We want both numbers to have the same exponent of \(10^6\):

To convert \(3.2 \times 10^4\) to \(10^6\), we can think of it like this:

Since \(10^6\) is 100 times bigger than \(10^4\), we move the decimal point two places to the left:

So, \(3.2 \times 10^4\) becomes \(0.032 \times 10^6\).

Step 2: Add the numbers

Now we add:

\(0.032 \times 10^6\) plus \(1.95 \times 10^6\)

We can just add the numbers in front, which are:

0.032 plus 1.95

This gives us:

1.982

So, we get:

1.982 times \(10^6\)

Final Answer

The sum of \(3.2 \times 10^4\) and \(1.95 \times 10^6\) is:

1.982 times \(10^6\)

That's it! Let me know if you need any more help!

Answer 10

can you not add so much symbols. no more symbols pls ez just answer the question without any symbols

Answer 11

Sure! Here’s the answer without any symbols:

First, we want to add three point two times ten to the fourth and one point ninety five times ten to the sixth.

To add these, we need to change three point two times ten to the fourth into the same form as one point ninety five times ten to the sixth.

We know that ten to the fourth is smaller than ten to the sixth. To convert it, we can write three point two times ten to the fourth as zero point zero three two times ten to the sixth.

Now we can add the two numbers:

Zero point zero three two plus one point ninety five is one point nine eight two.

So, the final answer is one point nine eight two times ten to the sixth.

Thank you for your patience! Let me know if you need anything else.