Home > Error Analysis > Error Analysis Multiplication By A Constant

# Error Analysis Multiplication By A Constant

## Contents

Bad news for would-be speedsters on Italian highways. That is it. The rule we discussed in this chase example is true in all cases involving multiplication or division by an exact number. The system returned: (22) Invalid argument The remote host or network may be down. http://axishost.net/error-analysis/error-analysis-multiplication.php

Constants If an expression contains a constant, B, such that q =Bx, then: You can see the the constant B only enters the equation in that it is used to determine If you are converting between unit systems, then you are probably multiplying your value by a constant. Mathematically, if q is the product of x, y, and z, then the uncertainty of q can be found using: Since division is simply multiplication by the inverse of a number, Square or cube of a measurement : The relative error can be calculated from    where a is a constant. http://lectureonline.cl.msu.edu/~mmp/labs/error/e2.htm

## Error Propagation Multiplication By A Constant

Exercises > 5. 4.3. How can you state your answer for the combined result of these measurements and their uncertainties scientifically? This is an example of correlated error (or non-independent error) since the error in L and W are the same.  The error in L is correlated with that of in W.  Solution: Use your electronic calculator.

This is easy: just multiply the error in X with the absolute value of the constant, and this will give you the error in R: If you compare this to the Multiplying by a Constant What would be your guess: can an American Corvette get away if chased by an Italian police Lamborghini?

The top speed of the Corvette A one half degree error in an angle of 90Â° would give an error of only 0.00004 in the sine. Standard Deviation Multiplication All rules that we have stated above are actually special cases of this last rule.

We will treat each case separately: Addition of measured quantities If you have measured values for the quantities X, Y, and Z, with uncertainties dX, dY, and dZ, and your final Please try the request again. The system returned: (22) Invalid argument The remote host or network may be down. Symbols used: independent variables: x, t and z dependent variable: y error: σ {\displaystyle \sigma } constant: C Contents 1 +-*/^ trig functions 1.1 Multiplying by a Constant 1.2 Adding &

The measured track length is now 50.0 + 0.5 cm, but time is still 1.32 + 0.06 s as before. Error When Multiplying By A Constant For example, if some number A has a positive uncertainty and some other number B has a negative uncertainty, then simply adding the uncertainties of A and B together could give The error propagation methods presented in this guide are a set of general rules that will be consistently used for all levels of physics classes in this department. Please try the request again.

## Multiplication Error Analysis Worksheet

The system returned: (22) Invalid argument The remote host or network may be down. http://physics.appstate.edu/undergraduate-programs/laboratory/resources/error-propagation v = x / t = 5.1 m / 0.4 s = 12.75 m/s and the uncertainty in the velocity is: dv = |v| [ (dx/x)2 + (dt/t)2 ]1/2 = Error Propagation Multiplication By A Constant General functions And finally, we can express the uncertainty in R for general functions of one or mor eobservables. Uncertainty Multiplication By A Constant For instance, in lab you might measure an object's position at different times in order to find the object's average velocity.

The derivative with respect to t is dv/dt = -x/t2. http://axishost.net/error-analysis/error-analysis-immunochemistry-error-analysis.php In order to convert the speed of the Corvette to km/h, we need to multiply it by the factor of 1.61. Your cache administrator is webmaster. Please see the following rule on how to use constants. Matrix Multiplication Constant

This is a starting point. Powers > 4.5. There is no way to develop intuition about the results. http://axishost.net/error-analysis/error-analysis-multiplication-division.php This is most easily done with calculus, but some parts of this can be done with algebra and even intuition.

The time is measured to be 1.32 seconds with an uncertainty of 0.06 seconds. Error Analysis Division None of these rules tells you which digit or decimal place to round to. If you measure the length of a pencil, the ratio will be very high.

## It could be anywhere between 9 and 11 feet wide.

The final result for velocity would be v = 37.9 + 1.7 cm/s. What should we do with the error? Products and Quotients > 4.3. Error Analysis Addition As in the previous example, the velocity v= x/t = 50.0 cm / 1.32 s = 37.8787 cm/s.

Knowing the uncertainty in the final value is the correct way to officially determine the correct number of decimal places and significant figures in the final calculated result. Please note that the rule is the same for addition and subtraction of quantities. This ratio is very important because it relates the uncertainty to the measured value itself. get redirected here Text is available under the Creative Commons Attribution-ShareAlike License.; additional terms may apply.

Example 1: Determine the error in area of a rectangle if the length l=1.5 ±0.1 cm and the width is 0.42±0.03 cm.  Using the rule for multiplication, Example 2: Advisors For Incoming Students Undergraduate Programs Pre-Engineering Program Dual-Degree Programs REU Program Scholarships and Awards Student Resources Departmental Honors Honors College Contact Mail Address:Department of Physics and AstronomyASU Box 32106Boone, NC Multiplying by a Constant if y = C ∗ x {\displaystyle y=C*x} then δ y = C ∗ δ x {\displaystyle {\delta _{y}}=C*{\delta _{x}}} proof Adding & Subtracting if y = The lowest possible top speed of the Lamborghini Gallardo consistent with the errors is 304 km/h.

which is not exactly the multiplication error performed twice Error Analysis Rounding Typically your instructor will choose which rounding rules to follow. Example: Suppose we have measured the starting position as x1 = 9.3+-0.2 m and the finishing position as x2 = 14.4+-0.3 m. So if the angle is one half degree too large the sine becomes 0.008 larger, and if it were half a degree too small the sine becomes 0.008 smaller. (The change which rounds to 0.001.

In the following examples: q is the result of a mathematical operation Î´ is the uncertainty associated with a measurement. Sums and Differences > 4.2. The highest possible top speed of the Corvette consistent with the errors is 302 km/h.