This document discusses significant figures and rounding numbers. It defines significant figures as the digits in a measurement that provide meaningful information about the measurement's precision or uncertainty. Numbers should be rounded so that only significant figures remain to avoid confusion. The document provides examples of how to determine significant figures and round measurements based on their level of uncertainty. It also outlines rules for operations like addition, subtraction, multiplication and division that preserve the appropriate number of significant figures. Finally, it distinguishes between accuracy, which refers to how close a measurement is to the true value, and precision, which refers to the reproducibility of measurements.
This topic, comparing numbers, illustrates how to compare one number or a group of numbers. It is the foundation for Algebra and the concepts used in that topic.
For a FREE online course on Numbers and Number Theory, visit step-above10.teachable.com. While there, check out our other course offerings.
Scatter diagrams, strong and weak correlation, positive and negative correlation, lines of best fit, extrapolation and interpolation. Aimed at UK level 2 students on Access and GCSE Maths courses.
This topic, comparing numbers, illustrates how to compare one number or a group of numbers. It is the foundation for Algebra and the concepts used in that topic.
For a FREE online course on Numbers and Number Theory, visit step-above10.teachable.com. While there, check out our other course offerings.
Scatter diagrams, strong and weak correlation, positive and negative correlation, lines of best fit, extrapolation and interpolation. Aimed at UK level 2 students on Access and GCSE Maths courses.
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2. SIGNIFICANT FIGURES It’sconsideredthatsignificantnumbers are thosenumbersthathave real meaningorprovidemeaning. Thesignificant figures of a number are determinedbyits error. These are significant figures thosewooccupy a position equaltoorabovetheorderor position of the error.
3. SIGNIFICANT FIGURES When expressed a number should beavoidedifthe use of sigificant figures, sinceit can be a source of confusion. Thenumbers should berounded so thatcontainonlysignificant figures
5. EXAMPLE Consider a measure of length that gives a value of 5432.4764 m with an error of 0.8 m. The error is therefore the order of tenths of a meter. It is clear that all numbers that occupy a number less than the tenth position provide no information. Indeed, what sense does it give the number to the nearest thousandths if we say that the error is about 1 meter?. The correct rounded number is 5432.5
6. THE RULE IN THE ROUNDING ARE Ifthe figure isignoredislessthan 5, iseliminated Ifthe figure iseliminated, itincreasesbyoneunitthedigitretained When thedigit removed is 5, last figure istaken as thenearestevenumber i.e. if the figure is even left on hold, and if it is odd, take the higher figure
7. RULES OF OPERATIONS WITH SIGNIFICANT FIGURES Rule 1: The experimental results are expressed with only a dubious figure, and with ± indicating uncertainty in measurement. Rule 2: The significant figures are counted from left to right, from the first nonzero digit digit and even doubtful.
8. RULES OF OPERATIONS WITH SIGNIFICANT FIGURES Rule 3: When you add or subtract two decimal numbers, the number of decimal digits of the result is equal to the amount with the least number of them.Note: One case of particular interest is the subtraction. Let us quote the following example: 30.3475-30.3472 = 0.0003 Note that each of the quantities have six significant figures and the result has only one. Subtracting significant figures are lost. This is important to keep in mind when working with calculators or computers where figures are to join and be subtracted. First there should be additions and subtractions then to lose the least possible number of significant figures.
9. RULES OF OPERATIONS WITH SIGNIFICANT FIGURES Rule 4: When you multiply or divide two numbers, the number of significant figures in the result is equal to the factor with fewer numbers.
10. EXACTITUD Y PRECISION Exactitude refers to how close it is measured or calculated value of the true value. Precision refers to how close an individual value is measured or calculated with respect to other
12. PRECISION Is related to the number of decimal places used to express the measured, whereas numerical methods are iterative techniques, expresses how close an approximation or an estimate value with respect to approximations or previous iterations of the same