What is the number of significant figures in each of the following measured quantities? (b) 3ⅹ10^-6 m

Verified step by step guidance

1. Identify the significant figures in the given number: 3\times10^{-6} m.
2. In scientific notation, the coefficient (the number before the multiplication sign) determines the significant figures.
3. The number '3' in the coefficient '3' has one significant figure.
4. The exponent '-6' in the scientific notation does not affect the number of significant figures.
5. Therefore, the number 3\times10^{-6} m has one significant figure.

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 ensuring that calculations reflect the precision of the data.

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. For example, 3 x 10^-6 m indicates a very small measurement, and understanding this format helps in identifying significant figures in such expressions.

Rules for Counting Significant Figures

There are specific rules for counting significant figures in measurements. For example, in scientific notation, all digits in the coefficient (the number before the exponent) are significant. Therefore, in the example 3 x 10^-6 m, the '3' is the only significant figure, leading to a total of one significant figure in this measurement.