how do you determine the last digit in any measured number?
I suppose the word you want is estimation.
6935.4721
To determine the last digit in any measured number, follow these steps:
1. Identify the unit of measurement: Determine what the measured number represents. For example, if the number is a length measured in inches, the unit of measurement is inches.
2. Determine the precision: Look at the measurement to determine its precision or the number of decimal places. If the measurement does not have any decimal places, disregard the following steps and the last digit is the rightmost digit in the measured number.
3. Look for the digit immediately to the right of the decimal point: This digit is the next digit after the unit digit and indicates the precision of the measurement.
4. Round the digit if needed: If the digit to the right of the decimal point is 5 or greater, round up the last digit in the measured number. If it is 4 or less, leave the last digit as it is.
For example, let's say you have a measurement of 2.378 inches. The unit of measurement is inches, and the precision is three decimal places. The digit immediately to the right of the decimal point is 3. Since it is less than 5, the last digit in the measured number remains unchanged, so the last digit is 8.
To determine the last digit in any measured number, you need to understand the concept of significant figures.
Significant figures are the meaningful digits in a number. The last digit is considered significant if it is certain or if it is estimated. However, there are a few rules to follow when determining the last digit based on significant figures:
1. Non-zero digits: All non-zero digits in a measured number are significant. For example, in the number 12.345, the last digit, 5, is significant.
2. Leading zeros: Leading zeros, which are zeros that appear before any non-zero digit, are not significant. They are only placeholders to indicate the decimal position. For example, in the number 0.00345, the last digit, 5, is significant, while the leading zeros, 00, are not.
3. Captive zeros: Captive zeros, which are zeros between non-zero digits, are always significant. For example, in the number 10.050, the last digit, 0, is significant.
4. Trailing zeros: Trailing zeros, which are zeros that appear after a non-zero digit and after the decimal point, are significant only if they are after a decimal point. For example, in the number 10.00, the last digit, 0, is significant because it is after the decimal point.
5. Whole numbers: In whole numbers without any decimal point, the last digit is always considered significant. For example, in the number 10000, the last digit, 0, is significant.
By following these rules, you can determine the last digit in any measured number based on significant figures.