Kristof bought a new terrarium, shaped like a rectangular prism, for his pet snake. The terrarium has a length of 1.8 × 10^2 cm, a width of 1.3 × 10^2 cm, and a height of 1.1 × 10^2 cm.

Question

Find the volume of the terrarium in scientific notation and in standard form. Answers should not be rounded.

The volume of the terrarium written in scientific notation is a × 10^b cubic cm, where a is Blank and b is Blank. The volume of the terrarium written in standard form is Blank
cubic cm.

Answer 1

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:

1. 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 \( 1.1 \):

\[ 2.34 \times 1.1 = 2.574 \]

2. Now, multiply the powers of ten:

\[ 10^2 \times 10^2 \times 10^2 = 10^{2+2+2} = 10^6 \]

3. 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.