The calculator below formats a number to the required significant figure and the scientific notation.

Rounding will be done using "round half to even" rule, also known as Gaussian rounding or banker's rounding:

Ignoring the positive or negative sign,

• Round up, if
• the next digit is greater than 5, or
• the next digit is 5 and there is a non-zero digit after, or
• the next digit is 5 and the current digit to be rounded is odd
• Round down, if
• the next digit is less than 5, or
• the next digit is 5 followed by only zero digits or not followed by any other digits and the current digit to be rounded is even

Please report any error to [email protected]

Please see below for the rules of significant figures and scientific notation.

#### Significant Figures

The significant figures (or significant digits) of a number are the digits that are known with some degree of confidence.

##### Rules for significant figures:
1. All non zero digits are significant.
E.g. $325$ has 3 significant figures, $52.34$ has 4 significant figures.

2. Zeros between non zero digits are significant.
E.g. $1009$ has 4 significant figures, $3.02$ has 3 significant figures.

E.g. $0.0005$ has 1 significant figure, $0.030$ has 2 significant figures.

4. Trailing zeros in a number containing a decimal point is significant.
E.g $25.00$ has 4 significant figures, $3.50$ has 3 significant figures.

5. Trailing zeros in a number not containing a decimal point can be either significant or insignificant. To indicate which zeros are significant, place a bar over the zeros which are significant or indicate the number of significant figures in the brackets.
E.g $2500$ has 2 significant figures, $35\overline{0}00$ has 3 significant figures, $120\overline{0}0$ has 4 significant figures, $800$ (2 sf) has 2 significant figures.
##### Rules for addition and subtraction:

The result of addition or subtration should have the same number of decimal places as the least number of decimal places in any number involved.

For example: $40.55+3.1+10.222=53.872$

The number with the least decimal places involved is $3.1$ (1 decimal place), therefore your result should be rounded to $53.9$ (3 significant figures).

##### Rules for multiplication and division:

The result of multiplication or division should have as many significant figures as the number involved which has the least number of significant figures.

For example: $\left(32.1×1.234\right)÷1.2=33.0095$

The number with the least number of significant figures is $1.2$ (2 significant figures). Therefore your result should be rounded to $33$ (2 significant figures).

#### Scientific Notation

Scientific Notation or standard form is a way of expressing a number in terms of power of ten. In other words, it's expressed in the form

$a×{10}^{n}$

where $a$ is a real number that satisfies $1\le |a|<10$ and $n$ is an integer. $a$ is called the significand and $n$ is called the exponent.

Please note that the absolute value of $a$ must be at least 1 and less than 10, hence $0.34×{10}^{2}$ and $-11.23×{10}^{4}$ are not in standard form.

Examples of converting numbers to scientific notation

• $1234$ becomes $1.234×{10}^{3}$
• $-0.000023$ becomes $-2.3×{10}^{-5}$
• $50000000$ becomes $5×{10}^{7}$

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