Question

Evaluate the following expressions in scientific notation.
(3.4 x 10^9) + (6.6x10^9)
(5.2 x 10^6) - (4.8 x 10^6)

Answer 1

To evaluate the expressions in scientific notation, we will follow the rules of adding and subtracting numbers in scientific notation.

1. **For (3.4 x 10^9) + (6.6 x 10^9)**:

Since both terms have the same exponent (10^9), we can add the coefficients directly:

\[
3.4 + 6.6 = 10.0
\]

Now, combining the result with the common exponent:

\[
10.0 x 10^9
\]

When we convert \(10.0\) into scientific notation, it is \(1.0 x 10^1\). Therefore:

\[
10.0 x 10^9 = (1.0 x 10^1) x 10^9 = 1.0 x 10^{1+9} = 1.0 x 10^{10}
\]

So,

\[
(3.4 x 10^9) + (6.6 x 10^9) = 1.0 x 10^{10}
\]

---

2. **For (5.2 x 10^6) - (4.8 x 10^6)**:

Again, both terms have the same exponent (10^6), so we can subtract the coefficients directly:

\[
5.2 - 4.8 = 0.4
\]

Now, combining the result with the common exponent:

\[
0.4 x 10^6
\]

To express \(0.4\) in scientific notation, we convert it to \(4.0 x 10^{-1}\). Therefore:

\[
0.4 x 10^6 = (4.0 x 10^{-1}) x 10^6 = 4.0 x 10^{-1 + 6} = 4.0 x 10^{5}
\]

So,

\[
(5.2 x 10^6) - (4.8 x 10^6) = 4.0 x 10^{5}
\]

---

**Final Answers:**
1. \( (3.4 x 10^9) + (6.6 x 10^9) = 1.0 x 10^{10} \)
2. \( (5.2 x 10^6) - (4.8 x 10^6) = 4.0 x 10^{5} \)