See also: numbers

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

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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.
   
   
3. Leading zeros are insignificant.
   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: $(32.1\times 1.234)÷1.2=33.0095$

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).

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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

$$a\times {10}^n$$

where $a$ is a real number that satisfies $1\le |<!--\; absolute\; bar\; -->a|<!--\; absolute\; bar\; --><10$ 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 $5\times {10}^7$

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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.

By Jimmy Sie

See also: numbers