Express 0.00005 in scientific notation.
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Enter the coefficient in the green box and the exponent in the yellow box.
Answer (2)
To express 0.00005 in scientific notation, we first convert it to 5.0 by moving the decimal point 5 places to the right. This gives us an exponent of -5. Therefore, the answer is 5 × 1 0 − 5 .
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Convert the number to a coefficient between 1 and 10: 0.00005 → 5.0 .
Count the number of decimal places the decimal point was moved: 5 places.
Determine the exponent of 10 based on the direction the decimal was moved (right is negative, left is positive): Since we moved to the right, the exponent is -5.
Express the number in scientific notation: 5 × 1 0 − 5 .
Explanation
Understanding Scientific Notation We need to express the number 0.00005 in scientific notation. Scientific notation is a way of writing numbers as a product of a number between 1 and 10 (the coefficient) and a power of 10.
Moving the Decimal Point To convert 0.00005 to scientific notation, we need to move the decimal point to the right until we have a number between 1 and 10. In this case, we move the decimal point 5 places to the right to get 5.0.
Determining the Exponent Since we moved the decimal point 5 places to the right, we need to multiply 5.0 by 1 0 − 5 to get the original number back. Therefore, 0.00005 in scientific notation is 5 × 1 0 − 5 .
Identifying Coefficient and Exponent The coefficient is 5 and the exponent is -5.
Final Answer Thus, 0.00005 expressed in scientific notation is 5 × 1 0 − 5 .
Examples
Scientific notation is extremely useful in various fields, especially in science and engineering, for representing very large or very small numbers. For example, the distance from the Earth to the Sun is approximately 150,000,000,000 meters, which can be written as 1.5 × 1 0 11 meters in scientific notation. Similarly, the size of a bacterium might be 0.000002 meters, which is 2 × 1 0 − 6 meters in scientific notation. Using scientific notation makes these numbers easier to work with and understand.
