Question

Add 3.2 x 104 + 1.95 x 10

Answer 1

Add 56 x 10-2 + 4.13 x 10-2

Answer 2

Subtract 1.95 x 106 - 3.2 x 104

Answer 3

Subtract 3.2 x 104 - 2.56 x 10-2

Answer 4

Multiply 8.03 x 10-8 x 2.56 x 10-2

Answer 5

Multiply 4.82 x 1012 x 3.2 x 104

Answer 6

To add the two numbers \( 3.2 \times 10^4 \) and \( 1.95 \times 10^1 \), we first need to express both numbers in the same exponential form.

We can convert \( 1.95 \times 10^1 \) to have the same exponent as \( 3.2 \times 10^4 \):

\[
1.95 \times 10^1 = 1.95 \times 10^1 \times \frac{10^3}{10^3} = 1.95 \times 10^4 \times 10^{-3} = 0.0195 \times 10^4
\]

Now we can add the two numbers in their equivalent forms:

\[
3.2 \times 10^4 + 0.0195 \times 10^4 = (3.2 + 0.0195) \times 10^4
\]

Now, perform the addition:

\[
3.2 + 0.0195 = 3.2195
\]

So, we now have:

\[
3.2195 \times 10^4
\]

Thus, the sum of \( 3.2 \times 10^4 + 1.95 \times 10^1 \) is:

\[
\boxed{3.2195 \times 10^4}
\]

Answer 7

To add the two numbers \( 56 \times 10^{-2} \) and \( 4.13 \times 10^{-2} \), we can simply add them together since they are already in the same exponential form.

\[
(56 + 4.13) \times 10^{-2}
\]

Now, perform the addition:

\[
56 + 4.13 = 60.13
\]

So we have:

\[
60.13 \times 10^{-2}
\]

This can also be expressed in decimal form:

\[
60.13 \times 10^{-2} = 0.6013
\]

Thus, the sum of \( 56 \times 10^{-2} + 4.13 \times 10^{-2} \) is:

\[
\boxed{60.13 \times 10^{-2}} \quad \text{or} \quad \boxed{0.6013}
\]

Answer 8

To subtract \( 1.95 \times 10^6 \) and \( 3.2 \times 10^4 \), we first need to express both numbers with the same exponent. We can convert \( 3.2 \times 10^4 \) to have the same exponent as \( 1.95 \times 10^6 \).

To do this, we'll express \( 3.2 \times 10^4 \) in terms of \( 10^6 \):

\[
3.2 \times 10^4 = 3.2 \times 10^4 \times \frac{10^2}{10^2} = 3.2 \times 10^6 \times 10^{-2} = 0.032 \times 10^6
\]

Now we can subtract:

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

Now, let's perform the subtraction:

\[
1.95 - 0.032 = 1.918
\]

So we have:

\[
1.918 \times 10^6
\]

Thus, the result of \( 1.95 \times 10^6 - 3.2 \times 10^4 \) is:

\[
\boxed{1.918 \times 10^6}
\]

Answer 9

To subtract \( 3.2 \times 10^4 \) and \( 2.56 \times 10^{-2} \), we need to express both numbers in the same exponential form. Let's convert \( 2.56 \times 10^{-2} \) to the same exponent as \( 3.2 \times 10^4 \).

We can express \( 2.56 \times 10^{-2} \) in terms of \( 10^4 \):

\[
2.56 \times 10^{-2} = 2.56 \times 10^{-2} \times \frac{10^{6}}{10^{6}} = 2.56 \times 10^{4} \times 10^{-6} = 0.0000256 \times 10^{4}
\]

Now we can subtract:

\[
3.2 \times 10^4 - 0.0000256 \times 10^4 = (3.2 - 0.0000256) \times 10^4
\]

Now we perform the subtraction:

\[
3.2 - 0.0000256 = 3.1999744
\]

So, we have:

\[
3.1999744 \times 10^4
\]

Thus, the result of \( 3.2 \times 10^4 - 2.56 \times 10^{-2} \) is approximately:

\[
\boxed{3.1999744 \times 10^4}
\]

In decimal form, this would be:

\[
\boxed{31999.744}
\]

Answer 10

To multiply the numbers \( 8.03 \times 10^{-8} \) and \( 2.56 \times 10^{-2} \), you can multiply the coefficients and then add the exponents.

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

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

Now, combine these results:

\[
20.5588 \times 10^{-10}
\]

For clarity, it's often standard to express numbers in scientific notation with a coefficient between 1 and 10. Therefore, we can rewrite \( 20.5588 \) as \( 2.055588 \times 10^1 \):

\[
20.5588 \times 10^{-10} = 2.055588 \times 10^1 \times 10^{-10} = 2.055588 \times 10^{-9}
\]

Thus, the final result of \( 8.03 \times 10^{-8} \times 2.56 \times 10^{-2} \) is:

\[
\boxed{2.055588 \times 10^{-9}}
\]

Answer 11

To multiply the numbers \( 4.82 \times 10^{12} \) and \( 3.2 \times 10^{4} \), you can follow these steps:

1. **Multiply the coefficients:**
\[
4.82 \times 3.2 = 15.424
\]

2. **Add the exponents:**
\[
12 + 4 = 16
\]

Now combine these results:

\[
15.424 \times 10^{16}
\]

To express it in proper scientific notation, we need the coefficient to be between 1 and 10. So, we can rewrite \( 15.424 \) as \( 1.5424 \times 10^1 \):

\[
15.424 \times 10^{16} = 1.5424 \times 10^1 \times 10^{16} = 1.5424 \times 10^{17}
\]

Thus, the final result of \( 4.82 \times 10^{12} \times 3.2 \times 10^{4} \) is:

\[
\boxed{1.5424 \times 10^{17}}
\]