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Homework Statement
if error was found out to be plus/minus 58 and observed value was 227.32 how should the data be rounded of( to which significant figure)
Significant figures are digits in a number that are considered to be accurate and reliable. They are used to express the precision of a number and indicate the amount of uncertainty in a measurement.
To round a number to a specific number of significant figures, you must first determine the rounding digit, which is the first non-zero digit to the right of the desired significant figures. Then, if the digit to the right of the rounding digit is 5 or greater, you round up the rounding digit. If it is less than 5, you leave the rounding digit as is. Finally, you drop all digits to the right of the rounding digit.
The error in this measurement is +/-58, meaning that the actual value could be 58 units higher or lower than the observed value of 227.32. This range of uncertainty is due to limitations in the measurement process and equipment used.
The number of significant figures in a measurement is determined by counting all digits from the first non-zero digit to the right until the last digit. Zeros between non-zero digits are also significant. Additionally, zeros to the left of the decimal point are not significant unless they are after a non-zero digit. Trailing zeros to the right of the decimal point are significant if they are measured or estimated values.
Rounding to significant figures is important in science because it allows for accurate and consistent reporting of data. It helps to avoid the appearance of false precision and ensures that the level of uncertainty in a measurement is conveyed. This is crucial in interpreting and comparing experimental results and making informed conclusions.