How To Find The Significant Figures Of A Number

In the previous example you should have noticed that the reply is presented in what is called scientific notation.

Scientific notation…

…is a mode to limited very small or very big numbers
…is most often used in "scientific" calculations where the assay must be very precise
…consists of two parts: A Number and a Power of 10. Ex: 1.22 x ten^three

For a number to be in correct scientific notation simply i digit may be to the left of the decimal. Then,

\begin{align} 1.22 & \times 10^3 \text{ is right} \\ 12.two & \times 10^two \text{ is non} \stop{marshal}

How to catechumen non-exponential numbers to exponential numbers:

Instance ane

$$ 234,999 $$

This is a large number and the implied decimal point is at the end of the number.

$$ 234,999. $$

To catechumen this to an exponential number we need to move the decimal to the left until simply one digit resides in front of the decimal betoken. In this number we move the decimal point five times.

$$ 2.34999 \text{ (five numbers)} $$

…and thus the exponent we place on the power of 10 is v. The resulting exponential number is and then:

$$2.34999 \times 10^5 $$

Other examples:

\begin{align} 21 & \to two.1 \times x^1 \\ 16600.01 & \to 1.660001 \times ten^4 \\ 455 & \to iv.55 \times 10^two \finish{align}

Small-scale numbers tin be converted to exponential notation in much the aforementioned style. You simply movement the decimal to the right until but one not-zero digit is in front of the decimal point. The exponent and then equals the number of digits you lot had to pass along the way.

Instance two

$$ 0.000556 $$

The first not-zero digit is 5 and then the number becomes 5.56 and we had to pass the decimal point by 4 digits to get information technology to the signal where there was just one non-zero digit at the forepart of the number then the exponent will be -4. The resulting exponential number is then:

$$ v.56 \times 10^{-4} $$

Other examples

\begin{align} 0.0104 & \to one.04 \times 10^{-ii} \\ 0.0000099800 & \to ix.9800 \times 10^{-six} \\ 0.1234 & \to 1.234 \times 10^{-1} \end{align}

Then to summarize, moving the decimal point to the left yields a positive exponent . Moving the decimal betoken to the right yields a negative exponent .

Another reason we often use scientific notation is to adjust the need to maintain the advisable number of meaning figures in our calculations.

Significant Figures

There are three rules on determining how many significant figures are in a number:

Non-zero digits are always pregnant.
Any zeros between two significant digits are significant.
A final zero or abaft zeros in the decimal portion ONLY are significant.

Examples

2003 has 4 significant figures
00.00300 has 3 significant figures
00067000 has 2 meaning figures
00067000.0 has half-dozen significant figures

Verbal Numbers

Verbal numbers, such as the number of people in a room, take an infinite number of significant figures. Verbal numbers are counting up how many of something are present, they are not measurements made with instruments. Some other example of this are defined numbers, such as

$$ 1 \text{ pes} = 12 \text{ inches} $$

In that location are exactly 12 inches in i foot. Therefore, if a number is exact, information technology DOES Non affect the accuracy of a calculation nor the precision of the expression. Some more examples:

In that location are 100 years in a century.
Interestingly, the speed of calorie-free is now a defined quantity. Past definition, the value is 299,792,458 meters per second.

In order to nowadays a value in the right number of meaning digits you will often accept to round the value off to that number of digits. Below are the rules to follow when doing this:

The awarding of pregnant figures rules while completing calculations is of import and there are unlike ways to apply the rules based on the type of adding being performed.

Significant Figures and Addition or Subtraction

In addition and subtraction the number of significant figures that tin be reported are based on the number of digits in the least precise number given. Specifically this ways the number of digits after the decimal determine the number of digits that can be expressed in the reply.

Instance

Significant Figures and Multiplication or Sectionalization

In multiplication and division the number of meaning figures is but determined past the value of everyman digits. This means that if you lot multiplied or divided three numbers: 2.one, 4.005 and 4.5654, the value 2.1 which has the fewest number of digits would mandate that the answer be given merely to 2 significant figures.