All the Sh*t You Should Have Learned by Paul Kleinman

All the Sh*t You Should Have Learned by Paul Kleinman

Author:Paul Kleinman
Language: eng
Format: epub
Publisher: Adams Media
Published: 2019-12-23T16:00:00+00:00


SCIENTIFIC NOTATION

WHAT IS SCIENTIFIC NOTATION? Scientific notation is a method of writing numbers that makes them easier to work with. These numbers can be of any value, and this system is typically used because the numbers are too big or too small. By simplifying normal decimal notation, one can then apply them to other equations and formulas with ease. This is a typical example of scientific notation:

x + 10y

x is a real number, and y is an integer representing how far you have to move the decimal point.

EXAMPLE OF SCIENTIFIC NOTATION Let’s look at a simple example of scientific notation:

3 ×104 = 30,000

The 3 can also be shown as 3.0 because there are no numbers following it. From there, we then have to move the decimal point an additional four spots. We move to the right, because the exponent is positive.

Similarly, to show the number 5,000 in scientific notation, it would look like this:

5 × 103

SCIENTIFIC NOTATION WITH NEGATIVE INTEGERS For negative integers, back the number of spaces the integer indicates. For example:

500 × 10-1 is equal to 50.

You start at 500, which can be shown as 500.0, and you move the decimal point to the left one space, making it 50. No matter how complex the number may appear, to turn a number into decimal notation, you must follow the exponent.

GOING FROM SCIENTIFIC NOTATION TO DECIMAL NOTATION To turn a number from decimal notation to scientific notation, you must work backward. You are starting with a number in decimal form, and want to end with the x × 10y equation. Make x as simple a number as you can between 1 and 10. So, for example:

0.003 would be equivalent to 3 × 10-3

And if the number is more complex, just remember to make it between 1 and 10. For example:

.002345 is just 2.345 × 10-3

ORDER OF MAGNITUDE The order of magnitude is a number rounded to the nearest power of 10. This enables simple comparisons, estimates, and rough calculations to be performed. So, for example, if something is 1.9 and you need to use it in a calculation, that number is closer to 100 than it is to 101, so when solving your problem, you would use 100.

ENGINEERING NOTATION Engineering notation is a form of scientific notation used in civil and mechanical engineering. It is slightly different than scientific notation. In engineering notation, the powers of 10 are restricted to be only multiples of 3. This is because they are actually powers of 1,000, so instead of writing 1,0002, it looks like 106.



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