What is the number of significant figures in each of the following measured quantities? (d) 2.94×10³ m²

Verified step by step guidance

1. Identify the digits in the number 2.94\times10^3.
2. Determine which digits are significant. In this case, all non-zero digits are significant.
3. Count the number of significant digits in the base number 2.94.
4. Recognize that the exponent in scientific notation (10^3) does not affect the number of significant figures.
5. Conclude that the number of significant figures in 2.94\times10^3 is the same as in 2.94.

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, 2.94×10³ indicates that the number is 2.94 multiplied by 1,000, which helps in identifying significant figures more easily.

Rules for Counting Significant Figures

There are specific rules for counting significant figures in a number. For example, in scientific notation, all digits in the coefficient (the number before the exponent) are significant. Therefore, in 2.94×10³, the digits 2, 9, and 4 are all significant, leading to a total of three significant figures in this measurement.