In the previous instance you should have actually noticed that the price is gift in what is referred to as scientific notation.

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Scientific notation…

…is a method to express very tiny or very large numbers…is most frequently used in "scientific" calculations whereby the evaluation must be very precise…consists of 2 parts: A Number and a strength of 10. Ex: 1.22 x 103

For a number to it is in in correct clinical notation only one digit might be come the left that the decimal. So,

\beginalign1.22 & \times 10^3 \text is correct \\12.2 & \times 10^2 \text is not\endalign

How to convert non-exponential numbers to exponential numbers:

Example 1

$$234,999$$

This is a large number and also the comprise decimal suggest is at the end of the number.

$$234,999.$$

To convert this to an exponential number we need to relocate the decimal to the left until just one digit stays in prior of the decimal point. In this number we relocate the decimal suggest 5 times.

$$2.34999 \text (five numbers)$$

…and thus the exponent we place on the strength of 10 is 5. The resulting exponential number is then:

$$2.34999 \times 10^5$$

Other examples:

\beginalign21 & \to 2.1 \times 10^1 \\16600.01 & \to 1.660001 \times 10^4 \\455 & \to 4.55 \times 10^2\endalign

Small numbers deserve to be convert to exponential notation in lot the same way. You just move the decimal come the best until only one non-zero digit is in front of the decimal point. The exponent then equals the variety of digits you had actually to pass follow me the way.

Example 2

$$0.000556$$

The very first non-zero digit is 5 so the number i do not care 5.56 and we had actually to happen the decimal point by 4 number to acquire it come the allude where there was just one non-zero number at the front of the number so the exponent will be -4. The result exponential number is then:

$$5.56 \times 10^-4$$

Other examples

\beginalign0.0104 & \to 1.04 \times 10^-2 \\0.0000099800 & \to 9.9800 \times 10^-6 \\0.1234 & \to 1.234 \times 10^-1\endalign

So come summarize, moving the decimal allude to the left yields a positive exponent. Relocating the decimal allude to the right returns a negative exponent.Another factor we frequently use scientific notation is come accommodate the require to keep the appropriate number of far-ranging figures in ours calculations.

### Significant Figures

There room three rule on determining exactly how many far-reaching figures room in a number:

Non-zero number are always significant.Any zeros in between two significant digits are significant.A last zero or trailing zeros in the decimal part ONLY are significant.

Examples

2003 has 4 significant figures00.00300 has actually 3 far-ranging figures00067000 has 2 far-ranging figures00067000.0 has 6 far-ranging figures

### Exact Numbers

Exact numbers, such together the number of people in a room, have an boundless number of far-ranging figures. Specific numbers are counting up how countless of something space present, they are not measurements made v instruments. One more example that this are defined numbers, such together

$$1 \text foot = 12 \text inches$$

There are exactly 12 customs in one foot. Therefore, if a number is exact, the DOES NOT impact the accuracy of a calculation no one the precision of the expression. Some more examples:

There space 100 years in a century.Interestingly, the rate of irradiate is currently a characterized quantity. Through definition, the value is 299,792,458 meters every second.

In bespeak to existing a value in the correct number of far-reaching digits you will frequently have to ring the worth off come that number of digits. Listed below are the rules to follow when doing this:

The application of far-reaching figures rules while completing calculations is important and there are different ways to apply the rules based upon the type of calculation gift performed.

### Significant figures and addition or Subtraction

In addition and subtraction the number of far-reaching figures that deserve to be reported are based upon the number of digits in the least specific number given. Particularly this method the variety of digits after the decimal determine the number of digits that deserve to be expressed in the answer.

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Example

### Significant Figures and Multiplication or Division

In multiplication and department the number of significant figures is simply figured out by the worth of shortest digits. This method that if you multiplied or split three numbers: 2.1, 4.005 and 4.5654, the worth 2.1 which has the fewest number of digits would certainly mandate the the answer be provided only to two far-reaching figures.