## Significant Figures and Scientific Notation

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

Rounding will be done using Gaussian rounding (also known as banker's rounding):

• 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

Enter a number

Number of significant figures

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 figures, 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, 35000 has 3 significant figures, 12000 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: ( 32.1 × 1.234 ) ÷ 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 × 10n

where a is a real number that satisfies 1 ≤ |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 × 102 and -11.23 × 104 are not in standard form.

Examples of converting numbers to scientific notation

• 1234 becomes 1.234 × 103
• -0.000023 becomes -2.3 × 10-5
• 50000000 becomes 5 × 107