3.2 x 10^4 + 1.95 x 10^6

Question

written in scintific notation

Answer 1

To add the numbers \(3.2 \times 10^4\) and \(1.95 \times 10^6\), we need to express them with the same exponent.

Let's convert \(3.2 \times 10^4\) to a form that has the same exponent as \(1.95 \times 10^6\):

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

Now we can add the two numbers:

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

Now, we have the sum:

\[ 1.982 \times 10^6 \]

So, \(3.2 \times 10^4 + 1.95 \times 10^6\) expressed in scientific notation is:

\[ 1.982 \times 10^6 \]

Answer 2

show your work regularly

Answer 3

Sure! Let's go through the process step by step to add \(3.2 \times 10^4\) and \(1.95 \times 10^6\) and express the result in scientific notation.

Step 1: Align the Exponents

To add these two numbers, we first need them to have the same exponent. The larger exponent is \(10^6\), so we will convert \(3.2 \times 10^4\) to use \(10^6\) as its exponent.

Convert \(3.2 \times 10^4\) to \(10^6\)

We can express \(10^4\) in terms of \(10^6\): \[ 10^4 = 10^6 \times 10^{-2} \]

Thus, we can rewrite \(3.2 \times 10^4\):

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

Step 2: Now We Can Add

Now that both terms are in terms of \(10^6\), we can add them together:

\[ 0.032 \times 10^6 + 1.95 \times 10^6 \]

Combine the coefficients:

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

Step 3: Write the Final Result

The sum \(3.2 \times 10^4 + 1.95 \times 10^6\) expressed in scientific notation is:

\[ \boxed{1.982 \times 10^6} \]

This concludes our work!