In which of the following pairs do both numbers contain the same number of significant figures?a. 0.005 75 g and 5.75 x 10⁻³ gb. 405 K and 405.0 Kc. 150 000 s and 1.50 x 10⁴ sd. 3.8 x 10⁻² L and 3.0 x 10⁻⁵ L

Verified step by step guidance

1. Identify the number of significant figures in each number of the given pairs.
2. For pair (a), count the significant figures in 0.005 75 g and 5.75 x 10^{-3} g.
3. For pair (b), count the significant figures in 405 K and 405.0 K.
4. For pair (c), count the significant figures in 150 000 s and 1.50 x 10^4 s.
5. For pair (d), count the significant figures in 3.8 x 10^{-2} L and 3.0 x 10^{-5} L.

Key Concepts

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. Understanding significant figures is crucial for accurately reporting measurements and performing calculations in chemistry.

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is represented as a product of a number between 1 and 10 and a power of ten. This notation helps in easily identifying significant figures, as the digits in the coefficient indicate the significant figures of the number.

Measurement Precision

Measurement precision refers to the degree to which repeated measurements under unchanged conditions show the same results. It is closely related to significant figures, as a higher number of significant figures indicates greater precision. Understanding precision is essential for comparing measurements and ensuring consistency in scientific data.