Question

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Explanation:

Step1: Convert 0.00032 to scientific notation

We know that to convert a decimal to scientific notation, we move the decimal point until there is one non - zero digit to the left of the decimal point. For 0.00032, we can write it as $3.2\times10^{-4}$. And we know that $10^{-3}=0.001$ and $10^{-4} = 0.0001$.

Step2: Analyze the position on the number line

The number line goes from 0 to $10^{-3}=0.001$. The value of $10^{-4} = 0.0001$, so $3.2\times10^{-4}=0.00032$ is 3.2 times $10^{-4}$. Since each small tick mark (assuming equal spacing) between 0 and $10^{-3}$ (which is 0.001) would represent an interval. Let's assume the number line from 0 to $10^{-3}$ is divided into 10 equal parts (since $10^{-3}\div10 = 10^{-4}$). So each part is $10^{-4}$. Then 0.00032 is 3.2 units of $10^{-4}$ from 0. So we start at 0 and move 3.2 tick marks (where each tick mark is $10^{-4}$) towards $10^{-3}$ to plot the point.

Since we can't actually plot the point here, but to describe the position: First, note that $0.00032=3.2\times10^{-4}$ and the number line has 0 at the left and $10^{-3}$ (0.001) at the right. The distance from 0 to $10^{-3}$ is 0.001. The value 0.00032 is 0.00032 units from 0. Since $0.00032\div(0.001\div10)=0.00032\div0.0001 = 3.2$, so we plot the point 3.2 tenths of the way from 0 to $10^{-3}$ (if we consider 10 equal divisions between 0 and $10^{-3}$).

Answer:

To plot point Q (0.00032) on the number line from 0 to $10^{-3}$ (0.001), we first recognize that $0.00032 = 3.2\times10^{-4}$ and $10^{-3}=10\times10^{-4}$. So we divide the segment from 0 to $10^{-3}$ into 10 equal parts (each part is $10^{-4}$). Then we move 3.2 of these parts (each of length $10^{-4}$) from 0 towards $10^{-3}$ and plot the point there. If we were to click on the graph, we would find the position that is 0.00032 units from 0 (or 3.2 times the length of the interval between 0 and the first tick mark, assuming the first tick mark is at $10^{-4}$) and place the point.