Tag: units and measurement: error analysis

Quizzes (17) Questions (163)

Questions Related to units and measurement: error analysis

Multiple choice physics units and measurement: error analysis rounding off digits rounding of digits standard form

The radius of the sun is $7\times 10^8 m$ and its mass is $2\times 10^{30} kg$. What is the order of magnitude of density of the sun?

  1. $1.4\times 10^3 kg/m^3$

  2. $ 10^7 kg/m^3$

  3. $1.5\times 10^3 kg/m^3$

  4. $10^3 kg/m^3$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given :  $R = 7\times 10^8 \ m$     and    $M = 2\times 10^{30} \ kg$
Volume of sun  $V = \dfrac{4}{3}\pi R^3 = \dfrac{4}{3}\pi\times (7\times 10^8)^3 = 1.4\times 10^{27} \ m^3$
Density of sun   $\rho = \dfrac{M}{V} = \dfrac{2\times 10^{30}}{1.4\times 10^{27}} = 1.43\times 10^3 \ kg/m^3$
Thus order of magnitude of density of sun is $10^3 \ kg/m^3$.

Multiple choice physics units and measurement: error analysis rounding off digits rounding of digits standard form

The radius of the earth is given $6.4\times 10^6 m$. What is the order of magnitude of the size of the earth? 

  1. $10^6 m$

  2. $6 \times 10^6 m$

  3. $10^7 m$

  4. $5 \times 10^6 m$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When a number rounded to the nearest power of 10, it is called order of magnitude. Here a number which is less than 5 is taken as 1 and a number greater than 5 is taken as 10. 
As $6.4>10, $ so it would be takes as 10. 
The order of magnitude of earth's size $=10\times 10^6=10^7 m$  

Multiple choice physics units and measurement: error analysis rounding off digits rounding of digits standard form

What is the order of magnitude of the distance of a quasar from us if light takes 2.9 billion years to reach us ?  

  1. $2.7\times 10^{25} m$

  2. $ 10^{25} m$

  3. $10^24 m$

  4. $3\times 10^{25} m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Here, time taken $t=2.9$ billion years $=2.9\times 10^9$ years $ =2.9\times 10^9\times (365\times 24\times 3600) s=9.14\times 10^{16} s$
Distance $=$ velocity $\times $ time
or $d=(3\times 10^8)\times (9.14\times 10^{16})=2.74\times 10^{25} m$
As $2.74 <5$ so it will be taken as 1. 
Thus, the order of magnitude of distance $d=1\times 10^{25} m=10^{25} m$

Multiple choice physics units and measurement: error analysis rounding off digits rounding of digits standard form

Match the following:

Column - I Column - II
A Deca p $10^3$
B Hecto q $10^6$
C Kilo r $10^1$
D Mega s $10^2$
E Giga t $10^8$
u $10^9$


  1. A-r, B-s, C-p, D-q, E-u

  2. <span>A-s, B-r, C-p, D-q, E-u</span>

  3. <span>A-r, B-s, C-u, D-q, E-p</span>

  4. <span>A-q, B-s, C-p, D-r, E-u</span>
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Here column-I represents the some prefixes and column-II represents the power of ten corresponding prefixes. 

Deca $=10^1$, hecto =$10^2$, kilo =$10^3$, mega $=10^6$, giga $=10^9$ 
Thus, A-r, B-s, C-p, D-q, E-u

Multiple choice physics units and measurement: error analysis rounding off digits rounding of digits standard form

With due regard to significant figures, add the following:
a. 953 and 0.324
b. 953 and 0.625
c. 953.0 and 0.324
d. 953.0 and 0.374

  1. a. $953$; b. $954$ c. $953.3$ d. $953.4$

  2. a. $953$; b. $955$ c. $953.3$ d. $953.4$

  3. a. $952$; b. $954$ c. $953.3$ d. $953.4$

  4. a. $953$; b. $954$ c. $953.3$ d. $952.4$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
a.  $953+0.324=953.324\approx \boxed { 953 } $
b.  $953+0.625=953.625\approx \boxed { 954 } $
c.  $953.0+0.324=953.324\approx \boxed { 953.3 } $
d.  $953.0+0.374=953.374\approx \boxed { 953.4 } $
Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

Write the number of significant digits in 0.6464 :

  1. 4

  2. 3

  3. 5

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

All non-zero numbers are always significant.All zeroes before a non zero number are insignificant. All zeroes which are simultaneously to the right of the decimal point and at the end of the number are significant. The only non significant digit here is the zero before the decimal point.
Hence, number of significant digits is 4.

Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

Write the number of significant digits in 6.032 ?

  1. 4

  2. 3

  3. 2

  4. none of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The significant figures of a number are those digits that carry meaning contributing to its measurement resolution. This includes all digits except:
1. All leading zeros;
2. Trailing zeros when they are merely placeholders to indicate the scale of the number (exact rules are explained at identifying significant figures); 
3. Spurious digits introduced, for example, by calculations carried out to greater precision than that of the original data, or measurements reported to a greater precision than the equipment supports.

According to rules,
$6.032$ 
All the digits are significant. (no leading and trailing zero)
No. of significant digits $= 4$

Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

The respective number of significant figures for the numbers 6.320, 6.032, 0.0006032 are then

  1. 3, 4, 8

  2. 4, 4, 8

  3. 4, 4, 4

  4. 4, 3, 4
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to the rules of significant figures $6.320$ has four significant figures.
$6.032$ has four significant figures.
$0.0006032$ has four significant figures.