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Scientific Notation
Scientific notation is the expression of a number based on the largest exponent of 10 for its value, where the form is a decimal number A x 10n.
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How is scientific notation done?
scientific notation is a method used to show very large numbers or very small numbers easily so for example say you want to put the number 579,000,000,000,000 into scientific notation you divide by ten until you get the decimal point behind the five then you show the other numbers behind the decimal point until you reach the long string of 0s (5.79) then multiply 5.79 by ten to the X power X being the number of times you divided by ten (5.79*10^14)
What is 293000 in scientific notation?
2.93E5, or 2.95 times 10 to the 5th power.
The difference between "scientific notation" and "engineering notation" is that scientific notation generally has one digit before the decimal point and can have any exponent, while engineering notation uses exponents divisible by 3; so, 3, 6, 9, 12 and so on. So in "engineering notation", this number would be 293 times 10 to the 3rd power, or 0.293 times ten to the sixth power.
What are the steps in using scientific notation?
Scientific notation is a way of representing numbers, usually very large or very small, in the form
a*10^b where 1<= |a| < 10 is adecimal number and b is an integer (negative or positive).
a is called the mantissa and b is called the exponent.
To convert a number to scientific notation:
- If the number has no decimal point, then add one at the end.
- Then move the decimal point to just after the first digit while counting the number of places you have moved it.
- The new number, formed after moving the decimal point is a.
- If the original number is negative, then so is a.
- The number of places to the left that the decimal point was moved is b. If it was moved to the right, then b is negative.
For example:
23045.06 becomes 2.304506*10^4
-23045.06 becomes -2.304506*10^4
0.00023004 becomes 2.3004*10^(-4)
To convert a number in scientific notation to normal form:
- If b is positive, move the decimal point b places to the right in the number a - adding 0s at the end of the number, if required.
- If b is negative, move the decimal point b places to the left in the number a - adding 0s immediately after the decimal point, if required.
- The final expression has the same sign (+ or -) as a in the scientific form.
For example:
4.56*10^5 = 456000.
-4.56*10^5 = -456000.
4.56*10^(-5) = 0.0000456
I have avoided using the term "Standard form" because, ironically, it is a non-standard term. In the UK Standard and Scientific forms are the same whereas in the US, the Standard form is what I have chosen to call the normal form.
What is 5 trillionths in scientific notation?
Trillionths is 10 to the power of - 12.
5 trillionths is equal to 5X10^(-12)
