Question

which of the following equations are true?

1.1x10^8/5.0x10^5=2.2x10^3
(3x10^4)-(2x10^4)=10000
12.01x10^-5/8.75x10^-6=1.375
(1.8x10^9)+(3.4x10^9)=5.2x10^9
(6.12x10^-3)x(4.25x10^-2)=1.37x10^-5

Answer 1

Let's evaluate each equation one by one to determine if they are true.

1. **\(1.1 \times 10^8 / 5.0 \times 10^5 = 2.2 \times 10^3\)**

Calculate the left side:
\[
\frac{1.1 \times 10^8}{5.0 \times 10^5} = \frac{1.1}{5.0} \times 10^{8-5} = 0.22 \times 10^3 = 2.2 \times 10^2
\]
So, the equation is **false**. The result is \(2.2 \times 10^2\) not \(2.2 \times 10^3\).

2. **\((3 \times 10^4) - (2 \times 10^4) = 10000\)**

Calculate the left side:
\[
(3 \times 10^4) - (2 \times 10^4) = 1 \times 10^4 = 10000
\]
The equation is **true**.

3. **\(12.01 \times 10^{-5} / 8.75 \times 10^{-6} = 1.375\)**

Calculate the left side:
\[
\frac{12.01 \times 10^{-5}}{8.75 \times 10^{-6}} = \frac{12.01}{8.75} \times 10^{-5+6} = \frac{12.01}{8.75} \times 10^{-(-1)}
\]
Calculate \( \frac{12.01}{8.75} \approx 1.373**.
Thus:
\[
1.373 \times 10^1 = 13.73, \text{ so the equation is false.}
\]

4. **\((1.8 \times 10^9) + (3.4 \times 10^9) = 5.2 \times 10^9\)**

Calculate the left side:
\[
(1.8 \times 10^9) + (3.4 \times 10^9) = (1.8 + 3.4) \times 10^9 = 5.2 \times 10^9
\]
The equation is **true**.

5. **\((6.12 \times 10^{-3}) \times (4.25 \times 10^{-2}) = 1.37 \times 10^{-5}\)**

Calculate the left side:
\[
(6.12 \times 10^{-3}) \times (4.25 \times 10^{-2}) = (6.12 \times 4.25) \times 10^{-3-2} = 26.005 \times 10^{-5}
\]
As \(26.005 \times 10^{-5}\) is approximately \(2.6005 \times 10^{-4}\), the equation is **false**.

### Summary of Results:
1. False
2. True
3. False
4. True
5. False

Thus, the true equations are 2 and 4.