Express each number in scientific notation. (a) 0.00000000007461 m (length of a hydrogen-hydrog

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Express each number in scientific notation. (a)...

Express each number in scientific notation. (a) $0.00000000007461 \mathrm{~m}$ (length of a hydrogen-hydrogen chemical bond) (b) $0.0000158 \mathrm{mi}$ (number of miles in an inch) (c) $0.000000632 \mathrm{~m}$ (wavelength of red light) (d) $0.000015 \mathrm{~m}$ (diameter of a human hair)

Express each number in scientific notation.
(a) $0.00000000007461 \mathrm{~m}$ (length of a hydrogen-hydrogen chemical bond)
(b) $0.0000158 \mathrm{mi}$ (number of miles in an inch)
(c) $0.000000632 \mathrm{~m}$ (wavelength of red light)
(d) $0.000015 \mathrm{~m}$ (diameter of a human hair)

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Key Concepts

Scientific Notation

Scientific notation is a method for expressing very large or very small numbers in a compact form by writing them as the product of a number (called the coefficient or mantissa) that lies between 1 and 10 and an integer power of 10. This notation simplifies arithmetic operations and highlights the magnitude of numbers, making it easier to compare sizes and manage significant figures.

Coefficient/Mantissa and Exponent

In scientific notation, the coefficient (or mantissa) is the part of the number that contains its significant figures, and it is multiplied by 10 raised to an exponent. The exponent indicates the number of places the decimal point has been moved: a positive exponent means the decimal is moved to the right (for large numbers), while a negative exponent means it is moved to the left (for small numbers).

Decimal Point Shifting

The process of converting a number to scientific notation involves shifting the decimal point so that the new number is between 1 and 10. The number of places the decimal is shifted becomes the absolute value of the exponent in the power of 10, with the sign of the exponent indicating the direction of the shift.

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