# 1.4 Significant figures  (Page 3/5)

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The question, now, is how to write a measurement of 50 cm in accordance with rule 5, so that it has decimal point to indicate that zeros are significant. We make use of scientific notation, which expresses a value in the powers of 10. Hence, we write different experiment values as given here,

$50\phantom{\rule{1em}{0ex}}cm=5.0X{10}^{1}\phantom{\rule{1em}{0ex}}cm$

This representation shows that the value has two significant figures. Similarly, consider measurements of 500 cm and 3240 cm as measured by an instrument. Our representation is required to reflect that these values have "3" and "4" significant figures respectively. We do this by representing them in scientific notation as :

$500\phantom{\rule{1em}{0ex}}cm=5.00X{10}^{2}\phantom{\rule{1em}{0ex}}cm$

$3240\phantom{\rule{1em}{0ex}}cm=3.240X{10}^{2}\phantom{\rule{1em}{0ex}}cm$

In this manner, we maintain the number of significant numbers, in case measurement value involves trailing zeros.

## Features of significant figures

From the discussion above, we observe following important aspects of significant figures :

• Changing units do not change significant figures.
• Representation of a value in scientific form, having power of 10, does not change significant figures of the value.
• We should not append zeros unnecessarily as the same would destroy the meaning of the value with respect to error involved in the measurement.

## Mathematical operations and significant numbers

A physical quantity is generally dependent on other quantities. Evaluation of such derived physical quantity involves mathematical operations on measured quantities. Here, we shall investigate the implication of mathematical operations on the numbers of significant digits and hence on error estimate associated with last significant digit.

For example, let us consider calculation of a current in a piece of electrical conductor of resistance 1.23 (as measured). The conductor is connected to a battery of 1.2 V (as measured). Now, The current is given by Ohm’s law as :

$I=\frac{V}{R}=\frac{1.2}{1.23}$

The numerical division yields the value as rounded to third decimal place is :

$⇒I=0.976\phantom{\rule{1em}{0ex}}A$

How many significant numbers should there be in the value of current? The guiding principle, here, is that the accuracy of final or resulting value after mathematical operation can not be greater than that of the operand (measured value), having least numbers of significant digits. Following this dictum, the significant numbers in the value of current should be limited to “2”, as it is the numbers of significant digits in the value of “V”. This is the minimum of significant numbers in the measured quantities. As such, we should write the calculated value of current, after rounding off, as:

$⇒I=0.98\phantom{\rule{1em}{0ex}}A$

## Multiplication or division

We have already dealt the case of division. We take another example of multiplication. Let density of a uniform spherical ball is 3.201 $gm/{\mathrm{cm}}^{3}$ and its volume 5.2 $gm/c{\mathrm{cm}}^{3}$ . We can calculate its mass as :

The density is :

$m=\rho V=3.201X5.2=16.6452\phantom{\rule{1em}{0ex}}gm$

In accordance with the guiding principle as stated earlier, we apply the rule that the result of multiplication or division should have same numbers of significant numbers as that of the measured value with least significant numbers.

#### Questions & Answers

A stone propelled from a catapult with a speed of 50ms-1 attains a height of 100m. Calculate the time of flight, calculate the angle of projection, calculate the range attained
Samson Reply
water boil at 100 and why
isaac Reply
what is upper limit of speed
Riya Reply
what temperature is 0 k
Riya
0k is the lower limit of the themordynamic scale which is equalt to -273 In celcius scale
Mustapha
How MKS system is the subset of SI system?
Clash Reply
which colour has the shortest wavelength in the white light spectrum
Mustapha Reply
how do we add
Jennifer Reply
if x=a-b, a=5.8cm b=3.22 cm find percentage error in x
Abhyanshu Reply
x=5.8-3.22 x=2.58
sajjad
what is the definition of resolution of forces
Atinuke Reply
what is energy?
James Reply
Ability of doing work is called energy energy neither be create nor destryoed but change in one form to an other form
Abdul
motion
Mustapha
highlights of atomic physics
Benjamin
can anyone tell who founded equations of motion !?
Ztechy Reply
n=a+b/T² find the linear express
Donsmart Reply
أوك
عباس
Quiklyyy
Sultan Reply
Moment of inertia of a bar in terms of perpendicular axis theorem
Sultan Reply
How should i know when to add/subtract the velocities and when to use the Pythagoras theorem?
Yara Reply
Centre of mass of two uniform rods of same length but made of different materials and kept at L-shape meeting point is origin of coordinate
Rama Reply

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 By By David Martin