Carry out the following operations and express the answers with the appropriate number of significant numbers. (c) (3.29×10⁴)(0.2501)

Verified step by step guidance

1. Identify the number of significant figures in each number: 3.29×10^4 has 3 significant figures, and 0.2501 has 4 significant figures.
2. When multiplying numbers, the result should have the same number of significant figures as the number with the fewest significant figures.
3. Multiply the numbers: (3.29×10^4) × (0.2501).
4. Determine the number of significant figures for the final answer based on the number with the fewest significant figures, which is 3 in this case.
5. Round the result to 3 significant figures to express the final answer.

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. When performing calculations, the result should reflect the least number of significant figures from the numbers involved in the operation to ensure accuracy.

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. A number is written as the product of a coefficient (between 1 and 10) and 10 raised to an exponent. This notation simplifies calculations, especially when dealing with very large or very small values, as seen in the example of 3.29×10^4.

Multiplication of Numbers in Scientific Notation

When multiplying numbers in scientific notation, you multiply the coefficients and add the exponents of the powers of ten. For example, in the operation (3.29×10^4)(0.2501), you first multiply 3.29 by 0.2501, then add the exponent of 10 from the first number to the exponent of 10 from the second number, ensuring the final result is expressed in proper scientific notation with the correct number of significant figures.