We need to know Scientific Notation before learning about Significant Figures.Lets dive into that first, and then we will move to Significant Figures and how to calculate the significant digits in numbers

In which any number can be represented in the form $N \times 10^n$ (Where n is an exponent having positive or negative values and N can vary between 1 to 10).

e.g. We can write $162.108$ as $1.62108 \times 10^2$ in scientific notation. Similarly, $0.00021$ can be written as $2.1 \times 10^{-4}$

\begin{align*} 1.1 \times 10^4 + 1.23 \times 10^3 &= 1.1 \times 10^{4} + .123 \times 10^{4}\\ &= 1.223 \times 10^4 \end{align*}

Suppose true value of quantity is \(3\) and two measurement taken are \(2.91 , 2.92\). They are precise as they close to each other but they are not accurate.

The measurement \(2.98\) and \(3.01\) are accurate as they are close to true value

- All non – zero digits are significant

For example : In \(185\) significant figure is \(3\)

\(2195\) significant figure - \(4\)

- Zero, proceeding to 1
^{st}non – zero digit are not significant. Such zero indicates the position of decimal point.

For example : 0.03 – significant figure 1 - Zero between non – zero digits are significant

For example : 2.005 – significant figure 4

1001 – significant figure 4

- All zeros placed to the right of a number are significant. For example, 16.0 has three significant figures, while 16.00 has four significant figures. Zeros at the end of a number without decimal point are ambiguous.
- In exponential notations, the numerical portion represents the number of significant figures. For example, $0.00045$ is expressed as $4.5 \times 10^{-4}$ in terms of scientific notations. The number of significant figures in this number is 2, while in Avogadro's number ($6.023 \times 10^{23}$ )it is four.

- If the digit coming after the desired number of significant figures happens to be more than 5, the preceding significant figure is increased by one, 5.318 is rounded off to 5.32
- If the digit involved is less than 5, it is neglected and the preceding significant figure remains unchanged, 4.312 is rounded off to 4.31.
- If the digit happens to be 5, the last mentioned or preceding significant figure is increased by one only in case it happens to be odd. In case of even figure, the preceding digit remains unchanged. 8.375 is rounded off to 8.38 while 8.365 is rounded off to 8.36.

- \(10.1 + 1.52 + 2.301 = 4.921\)

__Answer__\(4.9\) - \(2.52 + 1.11 + 2.222 = 5.852\)

__Answer__\(5.85\) - \(5.4 - 2.1\)

\(= 3.3\)

- \(2.210 \times 0.011\)

\(= .024312\)

\(= 0.024\) - \(1.01 \times 0.02\)

\(= 0.0202\)

\(= 0.02\) - \(\frac {4.24}{0.2}\)

\(= 21.2\)

\(=20\)

We also have a Worksheet on Significant Figures (link opens in new window). You can do significant figures related questions practice using this worksheet.

Round off up to 3 significant figure the below numbers

(a) 4.135

(b) 5.125

By following the rounding rules ,we get

(a) 4.14

(b) 5.12

Express the following in the scientific notation with 2 significant figures-

(a) 0.0023

(b) 586,00

(c) 100.0

(a) $2.3 \times 10^{-3}$

(b) $5.9 \times 10^{-4}$

(c) $1.0 \times 10^2$

Round 451.45 to four, three, and two significant digits

(a) 451.4

(b) 451

(c) 450

During calculations generally there is a need to convert units from one system to other. This is called

We know that

1 inch = 2.54 x 10

This is can be written as

1 inch/ 2.54 x 10

Or

2.54 x 10

The above two are called Unit factors and it can be used to convert unit from one system to another

**Notes**- Some Basic Concepts of Chemistry
- Physical States of matter
- Chemical Classification Of matter
- The International System of Units (SI units)
- Significant Figures
- Laws of Chemical Combination
- Atomic Mass
- Molecular Mass
- Mole Concept (Avogadro Constant) And Molar mass
- Gram Atomic Mass
- Gram Molecular Mass
- Percentage composition
- StioChiometry
- Mole Fraction
- Molarity Definition
- Molality Definition
- Normality Formula

**Questions**