Tag: standard form

Questions Related to standard form

The mass of a box measured by a grocer's balance is 2.3 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. The total mass of the box is:

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

  1. 2.3 kg

  2. 2.34 kg

  3. 2.340 kg

  4. 2.3403 kg

Show answer
Correct Option: A
Explanation:

Here, mass of the box, $m = 2.3 kg$
Mass of one gold piece, $m _1 = 20.15 g = 0.02015 kg$
Mass of other gold piece, $m _2 = 20.17 g = 0.02017 kg$
$\therefore$ Total mass = $m + m _1 +m _2 = 2.3 kg + 0.02015 kg +0.02017 kg = 2.34032 kg$
As the result is correct only upto one place of decimal, therefore, on rounding off, we get Total mass $= 2.3 kg$

A cube has a side of length 1.2 x $10^{-2}$. Its volume upto correct significant figures is

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

  1. 1.7 x $10^{-6}m^3$

  2. 1.73 x $10^{-6}m^3$

  3. 1.78 x $10^{-6}m^3$

  4. 1.732 x $10^{-6}m^3$

Show answer
Correct Option: A
Explanation:
Here
Length of the cube, $L =12 x10^{-2} m$
Volume of the cube, $V= (1.2 \times10^{-2} m)^3= 1.728 \times 10^{-6}m^3$
As the result can have only two significant figures, therefore, on rounding off, we get, $V. 1.7 \times 10^{-6} m^3$

The numbers 2.745 and 2.735 on rounding off to 3 significant figures will give:

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

  1. 2.75 and 2.74

  2. 2.74 and 2.73

  3. 2.75 and 2.73

  4. 2.74 and 2.74

Show answer
Correct Option: D
Explanation:

In 2.745, the digit to be rounded off (i.e., 4) is even, hence it should be left unchanged and in 2.735, the digit to be rounded off (i.e., 3) is odd, hence it should be increased by 1, i.e., changed to 4.

The numbers 3.845 and 3.835 on rounding off to 3 significant figures will give then

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

  1. 3.85 and 3.84

  2. 3.84 and 3.83

  3. 3.85 and 3.83

  4. 3.84 and 3.84

Show answer
Correct Option: D
Explanation:

The number 3.845 rounded off to three significant figures becomes 3.84 since the preceding digit is even. On the other hand, the number 3.835 rounded off to three significant figures becomes 3.84 since the preceding digit is odd.

Round off to $3$ significant figures, a) $20.96$
b) $0.0003125$

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

  1. $21.0: 312\times 10^{-4}$

  2. $21.0: 3.12\times 10^{-4}$

  3. $2.10: 3.12\times 10^{-2}$

  4. $210: 3.12\times 10^{-4}$

Show answer
Correct Option: B

The order of magnitude of 0.00701 is:

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

  1. -3

  2. -1

  3. 2

  4. 1

Show answer
Correct Option: A
Explanation:

the order of magnitude of $0.00701$ is $-3$

we know that,

  $ N=a\times {{10}^{b}} $

 $ 0.00701=7.01\times {{10}^{-3}} $

Where b is the order of magnitude

So, the order of magnitude is -3

Note: For taking the order of magnitude, the number should always be written in the scientific notation first.

Calculate area enclosed by a circle of diameter $1.06\ m$ to correct number of significant figures.

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

  1.  $ 0.883 m^2$

  2.  $ 0.0883 m^2$

  3.  $ 0.88333 m^2$

  4.  $ 0.8830 m^2$

Show answer
Correct Option: A
Explanation:

Area = $ \pi (\dfrac{d}{2})^2  $

$ \Rightarrow Area = \dfrac{22}{7}\times 0.53^2 = 0.882828 $
But, no of significant in diameter should be equal to the no. of significant in Area, so Ans is $ 0.883 m^2$

Subtract $2.5 \times {10}^{4}$ from $3.9 \times {10}^{5}$ and give the answer to correct number of significant figures.

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

  1.  $ 3.6\times 10^6$

  2.  $ 3.6\times 10^5$

  3.  $ 36\times 10^5$

  4.  $ 36\times 10^6$

Show answer
Correct Option: B
Explanation:

We have $ 3.9 \times 10^5- 2.5 \times 10^4$

 $ = 3.9 \times 10^5- 0.25 \times 10^5$
$ =3.65 \times 10^5$
But our answer should be rounded off upto two significant digits.
So the ans is $ 3.6\times 10^5$

The sum of the numbers $436.32$, $227.244$ and $0.301$ inappropriate significant figures is:

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

  1. $663.821$

  2. $664$

  3. $663.8$

  4. $663.82$

Show answer
Correct Option: B

How many order of magnitude are there in one million?

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

  1. 5

  2. 4

  3. 6

  4. None of above

Show answer
Correct Option: C
Explanation:

For the number 1,000,000, we will shift the decimal to the left, stopping just before the first digit of the number. The number of moves you make to the left is the order of magnitude. Since we moved it six times, there are six orders of magnitude of 1,000,000, meaning that you can multiply 10 six times and get 1,000,000