In chemistry, most of the time, we come across both, theoretical as well as experimental calculations. There are many methods which can help in handling these numbers conveniently and with minimal uncertainty.

**Scientific Notation**:

**Scientific Notation**:

Atoms and molecules have extremely low masses, but they are present in large numbers.

Chemists deal with the figures which are as large as \(602,200,000,000,000,000,000,000\)

They also have to deal with numbers as small as \( 0.00000000000000000000000166g \)

There are even other constants like speed of light, charges on particles which have numbers above these stated magnitudes. It is written as ‘SCI’ display mode in scientific calculators.

To help us in handling these numbers we use the following notation: **m** × 10** ^{n}**, which is,

**m**times ten raised to the power of

**n**. In this

**n**is an exponent having positive and negative values and

**m**is that number which varies from \(1.000…\)

The scientific notation \(578.677\)

In the same way \(0.000089\)

This helps us to to attain easier handling, better precision and accuracy while performing operations on numbers with high magnitudes.

**Uncertainty in Multiplication and Division**:

**Uncertainty in Multiplication and Division**:

__ __Same rules can be applied for multiplication and division as well.

For e.g: \((3.9~ × ~10^6)~×~(2.1~ ×~10^5)\)

= \((3.9 ~×~ 2.1) ~×~ (10^{11})\)

= \(11.31 ~× ~10^{11}\)

\(\frac{3.6~×~10^{-5}}{2.0~×~10^{-4}}\)

= \(1.8 ~×~10^{-1}\)

**Uncertainty in Addition and subtraction**:

**Uncertainty in Addition and subtraction**:

In these operations first of all we have to place these numbers in such a way that they have same exponents.

Therefore, when we add \(5.43 ~×~10^4\)

For example: \(5.43 \times 10^4 + 0.345 \times10^5 = (5.43 + (0.345\times 10))\times 10^4\)

In the case of subtraction,

\(5.43 \times 10^4 – 0.345 \times10^5 = (5.43 – (0.345\times 10))\times10^4\\\)

\(\\=(5.43 – 3.45)\times10^4 = 1.98 \times 10^4\)

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