Question

Numbers express in scientific notation can be added as long as they have a common power of 10 first let’s look at what this looks like when we convert each number into standard form and add so what would 3×10 7+2×10 power seven and then we have to write in three times blank +2 times blank blank plus blank and blank. What would the answer be?

Answer 1

To add the numbers \(3 \times 10^7\) and \(2 \times 10^7\), we first express them in standard form. Since both numbers share the same power of 10 (\(10^7\)), we can add their coefficients directly.

In standard form, these numbers can be written as:

\[
3 \times 10^7 = 30,000,000
\]
\[
2 \times 10^7 = 20,000,000
\]

Now, we add the two numbers:

\[
30,000,000 + 20,000,000 = 50,000,000
\]

Next, we need to convert the result back into scientific notation.

The sum \(50,000,000\) can be written in scientific notation as:

\[
5 \times 10^7
\]

Therefore, the full expression can be rewritten as:

\[
3 \times 10^7 + 2 \times 10^7 = (3 + 2) \times 10^7 = 5 \times 10^7
\]

In your request to fill in "three times blank + two times blank blank plus blank and blank," we can say:

- **First blank**: \(3\)
- **Second blank**: \(2\)
- **Third blank**: \(5\)
- **Fourth blank**: \(10^7\)

So the filled-in statement would be:
3 times \(10^7\) + 2 times \(10^7\) equals 5 times \(10^7\).