Question

1. in 1970, the number of televisions sold in the united states was about (1.2 \times 10^7). write this number in standard form.
2. in 1950, about 3,880,000 households in the united states had televisions. write this number in scientific notation.
3. find the volume of the cube shown at right. write the answer in both standard form and in scientific notation.

(image of a cube with side length (s = 4000) mm)

Explanation:

Question 25:

Step 1: Recall scientific to standard form

To convert \(1.2\times10^{7}\) to standard form, we know that \(10^{7}=10000000\). Multiply \(1.2\) by \(10000000\).
\(1.2\times10000000 = 12000000\)

Step 1: Recall standard to scientific form

To convert \(3880000\) to scientific notation, we move the decimal point to get a number between \(1\) and \(10\). We move the decimal point \(6\) places to the left to get \(3.88\).
So, \(3880000 = 3.88\times10^{6}\)

Step 1: Volume of a cube formula

The volume \(V\) of a cube with side length \(s\) is given by \(V = s^{3}\). Here, \(s = 4000\) mm.
\(V=(4000)^{3}\)

Step 2: Calculate \(4000^{3}\)

\(4000^{3}=4000\times4000\times4000 = 64000000000\) (standard form)

Step 3: Convert to scientific notation

To convert \(64000000000\) to scientific notation, we move the decimal point \(10\) places to the left to get \(6.4\). So, \(64000000000 = 6.4\times10^{10}\)

Answer:

\(12000000\)

Question 26: