Write each number in scientific notation. −0.00000000405

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Identify the given number: \(-0.00000000405\).

Count how many places the decimal point must move to the right to place it after the first nonzero digit. Here, the decimal moves 9 places to the right.

Rewrite the number as a product of a number between 1 and 10 and a power of 10. Since the decimal moved 9 places to the right, the power of 10 will be \(10^{-9}\).

Express the number in scientific notation as \(-4.05 \times 10^{-9}\).

Remember that the negative sign remains in front of the coefficient, and the exponent is negative because the original number is less than 1.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Scientific Notation

Scientific notation expresses numbers as a product of a number between 1 and 10 and a power of 10. It simplifies handling very large or very small numbers by shifting the decimal point and using exponents to indicate the shift.

Decimal Place Movement

To convert a number to scientific notation, move the decimal point to create a new number between 1 and 10. The number of places moved determines the exponent of 10, which is positive if moved left and negative if moved right.

Handling Negative Numbers in Scientific Notation

When converting negative numbers, the negative sign remains in front of the coefficient in scientific notation. The process of moving the decimal and determining the exponent is the same as for positive numbers.

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