In this problem, you will practice adding, subtracting, multiplying, and dividing numbers written in scientific notation. For each part, use the following numbers.

Question

3.2×104
1.95×106
8.03×10−8
2.56×10−2
4.82×1012

choose one of the scientific numbers from the list and add it to 32.8. Show your work

f. Choose one of the scientific numbers from the list and subtract it from 1,845.19 (or subtract 1,845.19 from the number you choose). Show your work.

g. choose one of the scientific numbers from the list and multiply it by 256.7. Show your work.

h. choose one of the scientific numbers from the list and divide it by 0.3 (or divide 0.3 by the number you choose). Show your work.

Answer 1

Let's solve each part step by step, using the scientific notation numbers provided.

Part e: Addition

Choose: \( 3.2 \times 10^4 \)

Convert \( 32.8 \) to scientific notation: \[ 32.8 = 3.28 \times 10^1 \]

Align the exponents for addition:
To add these two numbers, we can express \( 3.2 \times 10^4 \) in a way that aligns with \( 3.28 \times 10^1 \): \[ 3.28 \times 10^1 = 0.0328 \times 10^4 \]

Now add: \[ 3.2 \times 10^4 + 0.0328 \times 10^4 = (3.2 + 0.0328) \times 10^4 = 3.2328 \times 10^4 \]

Part f: Subtraction

Choose: \( 1.95 \times 10^6 \)

Subtract \( 1.95 \times 10^6 \) from \( 1,845.19 \). Convert \( 1,845.19 \) to scientific notation: \[ 1,845.19 = 1.84519 \times 10^3 \]

Align the exponents for subtraction:
Express \( 1.95 \times 10^6 \) in terms of \( 10^3 \): \[ 1.95 \times 10^6 = 1950 \times 10^3 \]

Now subtract: \[ 1.84519 \times 10^3 - 1950 \times 10^3 = (1.84519 - 1950) \times 10^3 \] Since \( 1.84519 \) is much smaller than \( 1950 \): \[ = (-1948.15481) \times 10^3 = -1.94815481 \times 10^6 \]

Part g: Multiplication

Choose: \( 8.03 \times 10^{-8} \)

Multiply this by \( 256.7 \): \[ 256.7 = 2.567 \times 10^2 \]

Now perform the multiplication: \[ (8.03 \times 10^{-8}) \times (2.567 \times 10^2) = (8.03 \times 2.567) \times (10^{-8} \times 10^2) \]

Calculate \( 8.03 \times 2.567 \): \[ 8.03 \times 2.567 \approx 20.58671 \] And combined with the powers of 10: \[ 10^{-8 + 2} = 10^{-6} \]

So, the result is: \[ 20.58671 \times 10^{-6} \approx 2.058671 \times 10^{-5} \]

Part h: Division

Choose: \( 4.82 \times 10^{12} \)

Divide this by \( 0.3 \): Convert \( 0.3 \) to scientific notation: \[ 0.3 = 3.0 \times 10^{-1} \]

Now perform the division: \[ \frac{4.82 \times 10^{12}}{3.0 \times 10^{-1}} = \frac{4.82}{3.0} \times 10^{12 - (-1)} = \frac{4.82}{3.0} \times 10^{12 + 1} \]

Calculate \( \frac{4.82}{3.0} \): \[ \frac{4.82}{3.0} \approx 1.60666667 \approx 1.607 \]

So, combining the results: \[ 1.607 \times 10^{13} \]

Summary of Results

e. \( 3.2328 \times 10^4 \)
f. \( -1.94815481 \times 10^6 \)
g. \( 2.058671 \times 10^{-5} \)
h. \( 1.607 \times 10^{13} \)

Answer 2

make it sound simpler without the advanced chratacters

Answer 3

Sure! Let's simplify the explanation and use plain text.

Part e: Addition

Choose: 3.2 × 10^4

Firstly, we need to convert 32.8 into scientific notation:

• 32.8 is the same as 3.28 × 10^1.

To add these two numbers, we have to align the powers of 10:

• Rewrite 3.2 × 10^4 as 32,000 (which is 3.2 × 10^4) and 32.8 as 0.0328 × 10^4.

Now we can add:

• 3.2 × 10^4 + 0.0328 × 10^4 = (3.2 + 0.0328) × 10^4 = 3.2328 × 10^4

So, the result is 3.2328 × 10^4.

Part f: Subtraction

Choose: 1.95 × 10^6

Now let's work with the number 1,845.19:

• Convert 1,845.19 into scientific notation: 1,845.19 is the same as 1.84519 × 10^3.

Next, convert 1.95 × 10^6 into a comparable format:

• This can be written as 1950 × 10^3 (because 1.95 × 10^6 is equal to 1,950,000).

Now we can subtract:

• 1.84519 × 10^3 - 1950 × 10^3 = (1.84519 - 1950) × 10^3. Since 1.84519 is much smaller than 1,950, this comes out to be negative:
• The result is approximately -1948.15481 × 10^3, which can be written as -1.94815481 × 10^6.

Part g: Multiplication

Choose: 8.03 × 10^-8

Now we multiply this by 256.7:

• First, convert 256.7 into scientific notation: 256.7 can be written as 2.567 × 10^2.

Now multiply:

• Multiply the two parts: (8.03 × 2.567) and (10^-8 × 10^2).

Calculating:

• 8.03 × 2.567 is approximately 20.58671.
• For the powers of 10: (-8 + 2) = -6.

Putting it all together gives us:

• 20.58671 × 10^-6, which is about 2.058671 × 10^-5.

Part h: Division

Choose: 4.82 × 10^12

Let’s divide this by 0.3:

• First, convert 0.3 into scientific notation, which is 3.0 × 10^-1.

Now divide:

• Divide: (4.82 ÷ 3.0) and (10^12 ÷ 10^-1).

Calculating:

• 4.82 ÷ 3.0 is about 1.60666667 (which we can round to 1.607).
• For the powers of 10: (12 - (-1)) = 13.

So the result is:

• 1.607 × 10^13.

Summary of Results

• e. 3.2328 × 10^4
• f. -1.94815481 × 10^6
• g. 2.058671 × 10^-5
• h. 1.607 × 10^13

If you have any questions or need further simplification, feel free to ask!