Explanation:

(b) In , the two zeroes before six are not siginificant and two zeroes on right side of 9 are significant figures. Hence, number of significant figures are four (6900).

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Explanation:

(b) In addition the result will be in least number of places after decimal.and minimum number of significant figure. The sum of the given numbers can be calculated as 663.821 . The number with least decimal places is 227.2 is correct to only one decimal place but in addition of numbers, the final result should be rounded off to one decimal place i.e., 664.

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Explanation:

(c) As we know that in multiplication or division, the final result should retain as many significant figures as are there in the original number with the least significant figures.

The significant figure in given numbers  and 2.5  are four and two respectivey so, density should be reported to two significant figures.

Density

As rounding off the number upto 2 significant figures, we get density .

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Explanation:

(d) Rounding off 2.745 upto 3 significant figures here IVth digit is 5 and its preceding is even, so no change in 4. Thus answer would be 2.74 . Rounding off 2.735 upto 3 significant figures, here IV digit is 5 and its preceding digit is 3 (odd). So 3 is increased by 1 answer become would be 2.74 .

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Explanation:

(a) If  is error in a physical quantity, then relative error is calculated as .

Given that,

Length

Breadth  Area

In significant figure rounding off to three significant digits, area

So,

Now rounding off up to one significant figure .

So, Area .

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Explanation:

(c) Tension  force

Surface tension

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Explanation:

(a) By applying the Rule of significant figure in multiplication and addition.

As given that,

(consider only significant figure value)

(rounding off to two significant figures.)

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Explanation:

(d) As given that,

So,

Rounding off upto two significant digit

(Let)

Rounding off upto one significant digit

(Let)

So, correct value of

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Explanation:

(c) It is given that Young's modulus  is,

dyne

So,  dyne

Convert meter to centimeter

dyne

dyne

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Explanation:

(d) Given that fundamental quantities are momentum , area  and time .

Let us consider the dimensional formula for

where  is dimensionless constant of proportionality.

Dimensions of energy  and Dimension of

momentum

Dimension of Area

Dimension of Time

Dimension of energy

Putting all the dimensions, value

By principle of homogeneity of dimensions,

So, Dimensional formula (of energy)

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