## A Human Hair Was Measured to be 8.0×10−4 inch Thick. A cat hair was measured to be 4.0×10−1 inch thick. How much greater is the thickness of?

The thickness of a cat hair (4.0×10^(-1) inch) is much greater than that of a human hair (8.0×10^(-4) inch). To determine how much greater, subtract the thickness of the human hair from the cat hair’s thickness:(4.0×10^(-1) inch) – (8.0×10^(-4) inch) = 0.3992 inches

So, the cat hair is approximately 0.3992 inches thicker than the human hair.

## Comparing Measurements in Scientific Notation

When comparing measurements expressed in scientific notation, we need to convert them to standard decimal form first before finding the difference. Let’s examine how much greater a cat hair’s thickness of 4.0×10−1 inch is compared to a human hair’s 8.0×10−4 inch.

Converting from Scientific Notation

Scientific notation represents numbers as:

## Coefficient x 10Exponent

To convert to decimal form, we move the decimal point left or right based on the exponent:

Human hair: 8.0×10−4 Move decimal 4 places left = 0.00008 inches

Cat hair: 4.0×10−1 Move decimal 1 place left = 0.4 inches

## Finding the Difference

Now we can subtract to find how much greater:

Cat hair: 0.4 inches Human hair: 0.00008 inches

0.4 – 0.00008 = 0.39992 inches

So the cat hair is 0.39992 inches greater in thickness.

## Checking the Work

We can verify this by entering the scientific notation values into a calculator and having it perform the subtraction. Doing this also gives a difference of 0.39992 inches.

Obtaining the same result confirms that we accurately converted the measurements out of scientific notation before calculating the difference between them.

Handling very small and large measurements in scientific notation form allows compact representation. But converting back to standard decimal form makes computation and comparison straightforward.

In summary, when comparing measurements in scientific notation, first convert to regular decimal form, then find the difference between the resulting decimal values.

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