If we ask you what your weight is, you can easily say it. However, if we ask you what the value of π exactly is, there is uncertainty in measurement. Isn’t it? In the subject of chemistry, a lot of times, we have to deal with both experimental and theoretical calculations. Therefore, we have to follow more than one methods to measure or calculate these number with minimum errors and uncertainty. In this chapter, we will deal with the concept of uncertainty in measurement.

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## Uncertainty in Measurement

Too often, we come across values that are close to each other and their average values. In such cases, we can say that the measurement is absolutely correct or precise. However, at times you may not experience this. At all those times, you will have to mention the uncertainty in measurement.

**Browse more Topics under Some Basic Concepts Of Chemistry**

- Atomic Mass and Molecular Mass
- Concentrations
- Dalton’s Atomic Theory
- Importance and Scope of Chemistry
- Laws of Chemical Combination
- Mole and Equivalent Weight
- Nature of Matter
- Percentage Composition
- Properties of Matter and Their Measurement
- Stoichiometry and Stoichiometric Calculations

Specifying this uncertainty is important as it will help you study the overall effect on output. We indicate uncertainty through significant figures. So, what are significant figures? A significant figure is the total number of digits in a number. It includes the last digit whose value is uncertain. Let us now look at the practical and scientific notation of uncertainty in measurement.

### Scientific Notation

We know that atoms and molecules have extremely low masses. However, we must not forget that they are present in massive numbers. Scientists have to deal with numbers that are as large as 123,456,789,101,110,000,000,987,000,870 and more.

Sometimes, they also have to deal with numbers as small as 0.00000000000000000000000166 g. Do you know what this is? Yes! It is the mass of Hydrogen atom. In science, there are other constants that have difficult figures. They include speed of light and charges on particles. So, how do we handle these numbers?

### Handling These Numbers

We use notation like m × 10^{n } while handling these numbers. Here, we signify m times ten raised to the power of n. In this, we can also see that n is an exponent that has positive and negative values and m is that number which varies from 1.000… and 9.999…

Similarly, we can write the scientific notion of 578.677 as 5.78677 × 10^{2}. In this, w move the decimal to the left by two spaces. If we move it three spaces to the left, the power of 10 becomes 3. In the same way, we can also write 0.000089 as 8.9 × 10^{–5}. In this, we move the decimal five places towards the right, (−5) is the exponent.

This method eases the handling for us and gives better precision. We arrive at results that are more accurate when we are dealing with high magnitude numbers.

**Uncertainty in Multiplication and Division**

__We can apply the same rules as above, for the methods of multiplication and division too. For e.g: (3.9 × 10__^{6}) × (2.1 × 10^{5}) = (3.9 × 2.1)(10^{6+}^{5}) = (3.9 × 2.1) × (10^{11}) = 11.31 × 10^{11}

## Solved Example for You

Q: Explain the uncertainty in addition and subtraction with an example.

Solution: In addition and subtraction, we need to place these numbers in such a way that they have same exponents. This will be the first step of our solution. Therefore, when we add 5.43 × 10^{4} and 3.45 × 10^{3}, we make the powers equal first. After that, we add and subtract the coefficients.

For example: 5.43 × 10^{4 }+ 0.345 × 10^{5 }= (5.43 + (0.345 × 10))×10^{4} = 8.88 × 10^{4}.

In the case of subtraction, 5.43 × 10^{4 }– 0.345 × 10^{5 }= (5.43–(0.345×10)) × 10^{4} = (5.43–3.45)×10^{4 }= 1.98 × 10^{4}

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