• About how much longer is the diameter of a grain of salt than the width of a human hair Grain of Salt (diameter) 3x10^-4 Human Hair (width) 8x10^-5

Answer 1

To compare the diameter of a grain of salt to the width of a human hair, we need to divide the diameter of the grain of salt by the width of the human hair.

Given:

• Diameter of a grain of salt = \(3 \times 10^{-4}\) meters
• Width of a human hair = \(8 \times 10^{-5}\) meters

Now, we can calculate the ratio:

\[ \text{Ratio} = \frac{\text{Diameter of grain of salt}}{\text{Width of human hair}} = \frac{3 \times 10^{-4}}{8 \times 10^{-5}} \]

To simplify this, we can calculate it as follows:

\[ \frac{3}{8} \times \frac{10^{-4}}{10^{-5}} = \frac{3}{8} \times 10^{1} = \frac{3}{8} \times 10 = \frac{30}{8} = 3.75 \]

Thus, the diameter of a grain of salt is about 3.75 times longer than the width of a human hair.

Answer 2

Explain

Answer 3

Certainly! Let's break down the comparison between the diameter of a grain of salt and the width of a human hair step-by-step.

1. Understanding the Measurements:

   • The diameter of a grain of salt is given as \(3 \times 10^{-4}\) meters. This means it is 0.0003 meters, or 0.3 millimeters.
   • The width of a human hair is given as \(8 \times 10^{-5}\) meters. This translates to 0.00008 meters, or 0.08 millimeters.

2. Setting Up the Ratio:

   • To find out how much longer the grain of salt's diameter is than the human hair's width, you can set up a ratio: \[ \text{Ratio} = \frac{\text{Diameter of grain of salt}}{\text{Width of human hair}} = \frac{3 \times 10^{-4}}{8 \times 10^{-5}} \]

3. Dividing the Numbers:

   • When you divide the two measurements, you can handle the coefficients (the numbers in front) and the powers of ten separately.
   • First, divide the coefficients: \(3\) (from the grain of salt) divided by \(8\) (from the human hair) gives: \[ \frac{3}{8} = 0.375 \]
   • Next, divide the powers of ten: \(\frac{10^{-4}}{10^{-5}} = 10^{-4 - (-5)} = 10^{-4 + 5} = 10^{1}\), which is \(10\).

4. Combining the Results:

   • Now you multiply the results together: \[ 0.375 \times 10 = 3.75 \]

5. Conclusion:

   • This means that the diameter of a grain of salt is about 3.75 times larger than the width of a human hair.

So, in summary, by setting up the division of the two measurements, we calculated a ratio that shows that a grain of salt’s diameter is 3.75 times longer than a human hair’s width.