Please you try to answer the following key question of chapter one
- What is finite precision
- List the source of error
- Define error measurements
- Define mathematical modeling
- Define Accuracy and precision
- change 35.625 in to binary system
1.Finite precision is decimal representation of a number which has been rounded or truncated. There are many casess where this may be necessary or appropria
2.* Approximation error
- Truncation/discretization error
- Converges error
* Roundoff error
3. Measurements of error also called observational error is the difference b/n a measured quantity & its true value. It includes random error (naturally occuring errors that are to be expected with any experment and systematic errors caused by a miscalibrated instrument that affects all measurements.
4. Mathematical modeling is the art of describing in symbolic language a real life system so that approximately correct predictions can be made regarding the behaviour or outcome of the system under varied circumstances of interest.
5. * Accuracy is refers to how closely a value agrees with the true value.
*Precision is refers to how closely the values agree with each other.
6. Integer part conversion
Reminder
35/2= 17 1
17/2=8 1
8/2=4 0
4/2=2 0
2/2=1 0
1/2=0 1
the most significant bit is at the bottom so write the digits from lower to upper =(100011)
The fractional part conversion
Integer part
0.625*2= 1.28 1
0.28*2=0.56 0
0.56*2=1.12 1
the most significant bit is at the top so write the digits from upper to lower =(101)
then combine the integer part conversion & fractional part conversion. The result become (100011.101)2
1.Finite Precision is decimal represenation of number which has been rounded or truncated.
2.#Approximation error
-tuncation /discretization error
-converges error
#Round off error
3.Measurement of error also called observation error is the difference between ameasured quantity and its true value .it include random error (naturally occuing error that are expected with any experiment and systematic errors caused by amiscalibrated.
4.Mathematical modelings is the art of describing symboling language areal life system so that approximately correct prediction can be made regarding behaviour or out come of the system .
5.Accuracy is refers to how closely values agree with the true value.
#Precision is refers to how closely values agree with each other .
6.integer part conversation.
35/2=17 reminder
1
17/2=8 1
8/2=4 0
4/2=2 0
2/2=1 0
1/2=0 1
significant write the digit frome lower to upper (100011)
fractional part conversation
integer part
0.625*2 =1.28 1
0.28*2=0.56 0
0.56*2=1.12 1
to write upper to lower (101)
the combination integer and fraction conversation result
(100011.101)2
1, finite presision is desimal representation of a number w/c has been rounded or truncated.
2, source of errors are 1,Approximation errors
a,Truncation/Discretization error
b,Convergence errors
2,roundoff errors
3, measurement error also called observasional error is the d/ce b/n a measured quantity & its true value it includes randam error (naturally occuring errors that are to be experment and systematice error caused by a miscalibrated instrument that affects all measurements
4, mathematical model is a description of a system using mathematical concepts and language. the process of developing a mathematical model is termed mathematical modeling.
5, Accuracy refers to how closely a value agrees with the true value.
precision refers to how closely values agree with each other.
6, Integral part remainder fractional part remainder
35/2=17 1 625/2=312 1
16/2=8 1 312/2=156 0
8/2=4 0 156/2=78 0
4/2=2 0 78/2=37 0
2/2=1 0 37/2=18 1
1/2=0 1 18/2=9 0
9/2=4 1
4/2=2 0
2/2=1 0
1/2=0 1
(100011.101)2
#1) Finite precision is decimal representation of a number which has been rounded or truncated.
#2) In general error can be classified based on their source numerical and non numerical error
Non numerical error Numerical error
- modeling error - round off error
- blunder and mistake - truncation error
- uncertainty in information and data - propufution error
#3) Measurements of error also called observational error is the difference b/n a measured quantity & its true value. It includes random error (naturally occurring errors that are to be expected with any experiment and systematic errors caused by a miscalibrated instrument that affects all measurements.
#4) Mathematical modeling is the art of describing in symbolic language a real life system so that approximately correct predictions can be made regarding the behavior or outcome of the system under varied circumstances of interest.
#5) Accuracy is refers to how closely a value agrees with the true value.
Precision is refers to how closely the values agree with each other.
#6) Integer part conversion
Reminder
35/2= 17 1
17/2=8 1
8/2=4 0
4/2=2 0
2/2=1 0
1/2=0 1
the most significant bit is at the bottom so write the digits from lower to upper =(100011)
The fractional part conversion
Integer part
0.625*2= 1.28 1
0.28*2=0.56 0
0.56*2=1.12 1
the most significant bit is at the top so write the digits from upper to lower =(101)
then combine the integer part conversion & fractional part conversion. The result become (100011.101)2
1.Finite precision is decimal representation of a number which has been rounded or truncated. There are many casess where this may be necessary or appropria
2.* Approximation error
- Truncation/discretization error
- Converges error
* Roundoff error
3. Measurements of error also called observational error is the difference b/n a measured quantity & its true value. It includes random error (naturally occuring errors that are to be expected with any experment and systematic errors caused by a miscalibrated instrument that affects all measurements.
4. Mathematical modeling is the art of describing in symbolic language a real life system so that approximately correct predictions can be made regarding the behaviour or outcome of the system under varied circumstances of interest.
5. * Accuracy is refers to how closely a value agrees with the true value.
*Precision is refers to how closely the values agree with each other.
6. Integer part conversion
Reminder
35/2= 17 1
17/2=8 1
8/2=4 0
4/2=2 0
2/2=1 0
1/2=0 1
the most significant bit is at the bottom so write the digits from lower to upper =(100011)
The fractional part conversion
Integer part
0.625*2= 1.28 1
0.28*2=0.56 0
0.56*2=1.12 1
the most significant bit is at the top so write the digits from upper to lower =(101)
then combine the integer part conversion & fractional part conversion. The result become (100011.101)2
1,finite presision is desimal representation of a number w/c has been rounded or truncated.
2, source of errors are 1,Approximation errors
a,Truncation/Discretization error
b,Convergence errors
2,roundoff errors
3, measurement error also called observasional error is the d/ce b/n a measured quantity & its true value it includes randam error (naturally occuring errors that are to be experment and systematice error caused by a miscalibrated instrument that affects all measurements
4, mathematical model is a description of a system using mathematical concepts and language. the process of developing a mathematical model is termed mathematical modeling.
5, Accuracy refers to how closely a value agrees with the true value.
precision refers to how closely values agree with each other.
6, Integral part remainder fractional part remainder
35/2=17 1 625/2=312 1
16/2=8 1 312/2=156 0
8/2=4 0 156/2=78 0
4/2=2 0 78/2=37 0
2/2=1 0 37/2=18 1
1/2=0 1 18/2=9 0
9/2=4 1
4/2=2 0
2/2=1 0
1/2=0 1
(100011.101)2
mohamed abdinasir civil section c ramit 1912/10
1
.finite precision is decimal representation of a number which has been rounded or truncated.
2
.round off error,truncation error ,absolute error ,relative error measured error
3.
measurement error is defined as the difference between the true or actual value and the measured value.
4.
The process of developing a mathematical model
is termed mathematical modeling.
5.
Accuracy refers to how closely a value agrees with the true value.
Precision refers to how closely values agree with each other
6.
100100.101