Is each number rounded to four significant figures? a. 156.852 b. 156.842 c. 156.849 d. 156.899

Verified step by step guidance

1. Identify the number of significant figures required, which is four in this case.
2. For each number, locate the first four significant figures starting from the left.
3. Check the digit immediately after the fourth significant figure to determine if rounding is necessary. If this digit is 5 or greater, round up the fourth significant figure by one.
4. Apply the rounding rule to each number: a. 156.852, b. 156.842, c. 156.849, d. 156.899.
5. Verify that each rounded number has exactly four significant figures and adjust if necessary.

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.

Rounding Rules

Rounding rules dictate how to adjust numbers to a specified number of significant figures. When rounding, if the digit following 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. Mastery of these rules is essential for correctly determining the significant figures in a number.

Decimal Places

Decimal places refer to the number of digits to the right of the decimal point in a number. When assessing significant figures, it is important to consider how many decimal places are present, as this can affect the rounding process. In the context of the question, ensuring that each number is rounded to four significant figures involves careful attention to both the digits and their placement relative to the decimal point.