Quiz Chapter 01.06: Propagation of Errors – Holistic Numerical Methods

1. If $A=3.56\pm 0.05$ and $B=3.25\pm 0.04$ , the values of $A+B$ are

6.81\leq A+B \leq 6.90

6.72\leq A+B \leq 6.90

6.81\leq A+B \leq 6.81

6.71\leq A+B \leq 6.91

2. A number $A$ is correctly rounded to $3.18$ from a given number $B$ . Then $\left| A-B \right| \leq C$ , where $C$ is

0.005

0.010

0.180

0.09999

3. Two number $A$ and $B$ are approximated as $C$ and $D$ , respectively. The relative error in $C \times D$ is given by

\left | \left ( \dfrac{A-C}{A} \right ) \right | \times \left | \left ( \dfrac{B-D}{B} \right ) \right |

\left | \left ( \dfrac{A-C}{A} \right ) \right | + \left | \left ( \dfrac{B-D}{B} \right ) \right |+\left | \left ( \dfrac{A-C}{A} \right ) \right | \times \left | \left ( \dfrac{B-D}{B} \right ) \right |

\left | \left ( \dfrac{A-C}{A} \right ) \right | + \left | \left ( \dfrac{B-D}{B} \right ) \right |-\left | \left ( \dfrac{A-C}{A} \right ) \right | \times \left | \left ( \dfrac{B-D}{B} \right ) \right |

\left ( \dfrac{A-C}{A} \right ) - \left ( \dfrac{B-D}{B} \right )

4. The formula for normal strain in a longitudinal bar is given by

$\epsilon = \dfrac{F}{AE}$

where

- - $F=$ normal force applied
  - $A=$ cross-sectional area of the bar
  - $E=$ Young’s modulus

If $F=50 \pm 0.5N$ , $A=0.2 \pm 0.002 m^{2}$ , and $E=210 \times 10^{9}Pa \pm 1 \times 10^{9}Pa$ , the maximum error in the measurement of strain is

10^{-12}

2.95\times 10^{-11}

1.22 \times 10^{-9}

1.19 \times 10^{-9}

5. A wooden block is measured to be 60 mm by a ruler and the measurements are considered to be good to 1/4th of a millimeter. Then in the measurement of 60 mm, we have ________ significant digits

0

1

2

3

6. In the calculation of the volume of a cube of nominal size $5"$ , the uncertainty in the measurement of each side is $10$ %. The uncertainty in the measurement of the volume most nearly is

5.477%

10.00%

17.32%

30.00%