Tag: rounding of digits

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

  1. 2.3 kg

  2. 2.34 kg

  3. 2.340 kg

  4. 2.3403 kg
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $= 2.3 kg$

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

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

  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 $10^{-6}m^3$
Reveal answer Fill a bubble to check yourself
A Correct answer
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, $V. 1.7 \times 10^{-6} m^3$
Multiple choice physics units and measurement: error analysis rounding off digits rounding of digits standard form

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

  1. 2.75 and 2.74

  2. 2.74 and 2.73

  3. 2.75 and 2.73

  4. 2.74 and 2.74
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

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

  1. 3.85 and 3.84

  2. 3.84 and 3.83

  3. 3.85 and 3.83

  4. 3.84 and 3.84
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

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

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

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

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

  4. $210: 3.12\times 10^{-4}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For 20.96, rounding to 3 significant figures gives 21.0. For 0.0003125, the first three significant digits are 3, 1, and 2; since the next digit is 5, we round up to 3.13 * 10^-4. Option B is the closest standard representation provided.

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

The order of magnitude of 0.00701 is:

  1. -3

  2. -1

  3. 2

  4. 1
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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

  1. <span>&nbsp;$ 0.883 m^2$</span>

  2. <span>&nbsp;$ 0.0883 m^2$</span>

  3. <span>&nbsp;$ 0.88333 m^2$</span>

  4. <span>&nbsp;$ 0.8830 m^2$</span>
Reveal answer Fill a bubble to check yourself
A Correct answer
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$

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

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

  1. <span>&nbsp;</span><span>$ 3.6\times 10^6$</span>

  2. <span>&nbsp;</span><span>$ 3.6\times 10^5$</span>

  3. <span>&nbsp;</span><span>$ 36\times 10^5$</span>

  4. <span>&nbsp;</span><span>$ 36\times 10^6$</span>
Reveal answer Fill a bubble to check yourself
B Correct answer
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$

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

How many order of magnitude are there in one million?

  1. 5

  2. 4

  3. 6

  4. None of above
Reveal answer Fill a bubble to check yourself
C Correct answer
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