*See also: numbers*

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.

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

- All non zero digits are significant.

E.g. $325$ has 3 significant figures, $52.34$ has 4 significant figures. - Zeros between non zero digits are significant.

E.g. $1009$ has 4 significant figures, $3.02$ has 3 significant figures. - Leading zeros are insignificant.

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

*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).

*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: $(32.1\times 1.234)\xf71.2=33.0095$

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** 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

where $a$ is a real number that satisfies $1\le \left|a\right|<10$ 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 $0.34\times {10}^{2}$ and $-11.23\times {10}^{4}$ are not in standard form.

Examples of converting numbers to scientific notation

- $1234$ becomes $1.234\times {10}^{3}$
- $-0.000023$ becomes $-2.3\times {10}^{-5}$
- $50000000$ becomes $5\times {10}^{7}$

Confused and have questions? We’ve got answers. With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field.

*See also: numbers*