To find the volume of the terrarium, which is shaped like a rectangular prism, we use the formula for the volume \( V \):
\[ V = \text{length} \times \text{width} \times \text{height} \]
Given:
- Length \( = 1.8 \times 10^2 \) cm
- Width \( = 1.3 \times 10^2 \) cm
- Height \( = 1.1 \times 10^2 \) cm
Now, we can calculate the volume step by step:
- Multiply the coefficients:
\[ 1.8 \times 1.3 \times 1.1 \]
Calculating this:
\[ 1.8 \times 1.3 = 2.34 \]
Now multiply \( 2.34 \) by \( 1.1 \):
\[ 2.34 \times 1.1 = 2.574 \]
- Now, multiply the powers of ten:
\[ 10^2 \times 10^2 \times 10^2 = 10^{2+2+2} = 10^6 \]
- Therefore, the volume in scientific notation is:
\[ V = 2.574 \times 10^6 \text{ cubic cm} \]
Next, let's convert this into standard form:
\[ 2.574 \times 10^6 = 2574000 \text{ cubic cm} \]
Putting everything together:
The volume of the terrarium written in scientific notation is:
- \( a = 2.574 \)
- \( b = 6 \)
The volume of the terrarium written in standard form is:
- \( 2574000 \text{ cubic cm} \)
Thus, the final answers are:
- \( a = 2.574 \)
- \( b = 6 \)
- Standard form: 2574000 cubic cm.