Express the following measurements in scientific notation. (b) 0.000 042 1 mL

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Identify the significant figures in the given measurement: 0.000 042 1 mL. The significant figures are 4, 2, and 1.

Determine the position of the decimal point in the original number. It is located after the first three zeros.

Count the number of places the decimal point needs to move to the right to get a number between 1 and 10. In this case, it needs to move 5 places.

Express the number as a product of a number between 1 and 10 and a power of 10. The number is 4.21, and the power of 10 is determined by the number of places the decimal moved, which is \(10^{-5}\).

Combine the number and the power of 10 to express the measurement in scientific notation: \(4.21 \times 10^{-5}\) mL.

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Scientific Notation

Scientific notation is a method of expressing numbers that are too large or too small in a more manageable form. It is written as the product of a number between 1 and 10 and a power of ten. For example, the number 0.0000421 can be expressed as 4.21 x 10^-5, which simplifies calculations and comparisons.

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02:50

Standard Notation to Scientific Notation

Significant Figures

Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. When converting to scientific notation, it is important to retain the correct number of significant figures to accurately represent the precision of the original measurement.

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Significant Figures Example

Decimal to Scientific Conversion

Converting a decimal number to scientific notation involves identifying the first non-zero digit and counting how many places the decimal point must move to the right or left to place it after this digit. This movement determines the exponent of ten. For instance, moving the decimal in 0.0000421 four places to the right results in an exponent of -5, leading to the final expression of 4.21 x 10^-5.

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