Measured Number and Significant Figures Lesson

  • Measured Numbers: Are the numbers obtained when you measure a quantity such as your height, weight, or temperature.

  • To write a measured number

    • Observe the numerical values of the marked lines

    • Estimate the value of the number between the marks

    • The estimated number is the final number in your measured number.

Measuring Using Estimated Digits

  • Certain Digits: Digits that can be identified as certain due it marking on a ruler.

  • Plus estimate: Adding a decimal values past certain digits in estimation.

  • Every measurement should include an estimated digit. Estimate the number between the lines.

  • When you look at a measurement, you know that the last digit is always estimated and has the most uncertainty.    

Significant Figures

  • Are used to represent the amount of error associated with a measurement.

  • All are nonzero digits and zeros between digits.

  • Are not zeros that act as a placeholder before digits.

  • Are zeros at the end of a decimal number.

  • How to know if a number is a significant figure

    • A non zero digits: All digits from 1 to 9 are significant

    • Zeros may or may not be significant: How to know:

      • Preceeding zeros - Never significant

      • Trapped Zeros - Always significant

      • Following zeros - significant if there is a decimal in the number

Exact Numbers

Exact Numbers Are

  • Numbers obtained by counting

    • 8 cookies

  • Definitions that compare two units

    • 1 Quart = 4 Cups

  • Definitions in the same measuring system

    • 1 KG = 1000 G

  • Exact numbers are not measured and do not have a limited number of significant figures.

  • Not used to find the number of significant figures in a calculated answer.

Rules for Rounding Off

  • If the first digit to be dropped is four or less, then it and all the following digits are dropped from the number.

  • If the digit to be dropped is 5 or greater, and there are more digits after it, then the last retained digit of the number is increased by 1.

  • If the first digit to be dropped is 5 and there are no more digits following it, you round the last retained digit to get an even number. It could be rounded. It could be rounded up sometimes and rounded down sometimes.

Significant Figures

  • In multiplication or division, the final answer is written so that it has the same number it has the same number of significant figures as the measurement with the fewest significant figures.

    • Ex. 24.66 cm × 0.35 cm = 8.631 = 8.6 cm²

Adding Significant Zeros

  • Adding Zeros: When the calculator display contains fewer significant figures than needed, add one or more to obtain the correct number of significant figures.

    • Ex. 6.0/2.00 = 3.00

Addition and Subtraction

  • In addition or subtraction, the final answer is written so that it has the same number of decimal places as the measurement with the fewest decimal places.

    • ex. 2.012 + 61.08 + 3.0 = 66.102 = 66.1