Perform each of the following calculations, and give an answer with the correct number of significant figures:
b. 0.00278 × 5

Verified step by step guidance

1. Identify the number of significant figures in each value. For 0.00278, there are 3 significant figures (the leading zeros are not significant). For 5, it is ambiguous, but if no decimal point is shown, it is typically considered to have 1 significant figure.
2. Perform the multiplication: Multiply 0.00278 by 5. The raw result will be calculated, but do not round it yet.
3. Determine the number of significant figures for the final answer. The result of a multiplication or division should have the same number of significant figures as the value with the fewest significant figures. In this case, the value with the fewest significant figures is 5, which has 1 significant figure.
4. Round the raw result to 1 significant figure, as determined in the previous step.
5. Express the final answer in proper scientific notation if necessary, ensuring it reflects the correct number of significant figures.

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 calculations in scientific contexts.

Multiplication Rules for Significant Figures

When multiplying numbers, the result should be reported with the same number of significant figures as the factor with the least significant figures. This rule ensures that the precision of the result reflects the precision of the least precise measurement involved in the calculation.

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small in a compact form, using powers of ten. It is particularly useful in scientific calculations to maintain significant figures and simplify arithmetic operations. For example, 0.00278 can be expressed as 2.78 x 10^-3.