Question
A marine biologist discovered a species with a diameter of 0.0000000000000836 inches. Express this measurement using scientific notation. You must show ALL work to earn full credit.
Answers
GPT-4o mini
To express the diameter of the newly discovered species in scientific notation, we need to convert the number \(0.0000000000000836\) into a form such that it is represented as \(a \times 10^n\), where \(1 \leq a < 10\) and \(n\) is an integer.
**Step 1: Identify the decimal point's movement**
1. The original number is: \(0.0000000000000836\)
2. To express this in scientific notation, we want to move the decimal point to the right until we have a number between 1 and 10.
3. The decimal point is currently located at the beginning (0.0000000000000836).
4. We move the decimal point to the right past the leading zeros, stopping after the first non-zero digit, which is `8`.
**Step 2: Count the number of places moved**
1. We move the decimal point 13 places to the right, from \(0.0000000000000836\) to \(8.36\).
**Step 3: Determine the power of ten**
1. Since we moved the decimal point to the right, we will have a negative exponent.
2. Therefore, we denote this movement as \(10^{-13}\).
**Step 4: Combine the numbers to form scientific notation**
1. The number in scientific notation is \(8.36 \times 10^{-13}\).
Thus, the diameter of the species expressed in scientific notation is:
\[
\boxed{8.36 \times 10^{-13}}
\]
**Step 1: Identify the decimal point's movement**
1. The original number is: \(0.0000000000000836\)
2. To express this in scientific notation, we want to move the decimal point to the right until we have a number between 1 and 10.
3. The decimal point is currently located at the beginning (0.0000000000000836).
4. We move the decimal point to the right past the leading zeros, stopping after the first non-zero digit, which is `8`.
**Step 2: Count the number of places moved**
1. We move the decimal point 13 places to the right, from \(0.0000000000000836\) to \(8.36\).
**Step 3: Determine the power of ten**
1. Since we moved the decimal point to the right, we will have a negative exponent.
2. Therefore, we denote this movement as \(10^{-13}\).
**Step 4: Combine the numbers to form scientific notation**
1. The number in scientific notation is \(8.36 \times 10^{-13}\).
Thus, the diameter of the species expressed in scientific notation is:
\[
\boxed{8.36 \times 10^{-13}}
\]