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The diameter of a human hair varies by color. The palest blond hair has a diameter of about 0.0017 centimeters while a black hair has a diameter of about 0.018 centimeters. What is each of these numbers written in scientific notation? Explain your answer.

User Trojanfoe
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Scientific notation is a way of expressing numbers that are very large or very small in a concise and standardized format. It consists of two parts: a coefficient and a power of 10.

To write a number in scientific notation, we express it as a product of a number between 1 and 10 (coefficient) and a power of 10. The coefficient should be greater than or equal to 1 and less than 10.

Let's convert the given hair diameters into scientific notation:

1. Palest blond hair diameter: 0.0017 centimeters

To convert it to scientific notation, we can express 0.0017 as 1.7 multiplied by a power of 10. We count the number of decimal places needed to shift the decimal point until we have a coefficient between 1 and 10.

0.0017 = 1.7 × 0.001

Since we moved the decimal point three places to the right, the power of 10 is -3.

Therefore, the palest blond hair diameter in scientific notation is:

0.0017 centimeters = 1.7 × 10^(-3) centimeters

2. Black hair diameter: 0.018 centimeters

Similarly, we can express 0.018 as 1.8 multiplied by a power of 10. This time, we only need to shift the decimal point one place to the right.

0.018 = 1.8 × 0.01

Since we moved the decimal point two places to the right, the power of 10 is -2.

Therefore, the black hair diameter in scientific notation is:

0.018 centimeters = 1.8 × 10^(-2) centimeters

In summary:

The palest blond hair diameter is written in scientific notation as 1.7 × 10^(-3) centimeters.

The black hair diameter is written in scientific notation as 1.8 × 10^(-2) centimeters.

User Shivang MIttal
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