Round off the following quantities to the number of significant figures indicated in parentheses. (a) 35,670.06 m (4, 6)

Verified step by step guidance

1. Identify the number of significant figures required for each part: (a) 4 significant figures, (b) 6 significant figures.
2. For part (a) with 4 significant figures, start from the left and count four digits. The number is 35,670.06, so the first four significant figures are 3, 5, 6, and 7.
3. Round the number to the fourth significant figure. Since the digit following the fourth significant figure (0) is less than 5, you do not need to round up.
4. For part (b) with 6 significant figures, start from the left and count six digits. The number is 35,670.06, so the first six significant figures are 3, 5, 6, 7, 0, and 0.
5. Round the number to the sixth significant figure. Since the digit following the sixth significant figure (6) is greater than 5, round up the last 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 calculations in scientific contexts.

Rounding Rules

Rounding rules dictate how to adjust numbers to the desired level of precision. When rounding, if the digit to the right of the last significant figure is less than 5, the last significant figure remains unchanged. If it is 5 or greater, the last significant figure is increased by one. These rules ensure that the rounded number reflects the appropriate level of accuracy.

Measurement Units

Measurement units provide a standard for quantifying physical quantities. In this question, the unit 'm' stands for meters, which is a fundamental unit of length in the International System of Units (SI). Understanding the context of measurement units is essential for interpreting and communicating scientific data accurately.