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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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What does exponential notation mean?
Exponential or "Scientific" notation is a way of writing numbers that are too big or too small to be conveniently written in decimal form. To overcome this one expresses the number and the power of 10 to which that number has to be raised.
Here are some examples:
Number -------------Exponential form
2 -------------------2×100
0.2 -----------------2×10−1
400 ----------------4×102
6,730,000,000 ------6.73×109
0.00000000773 -----7.73×10−9
What requires scientific notation?
Scientific notation is required for very large or very small numbers.
How do you put 1236840 in scientific notation?
- Find the decimal point (if there is not one visible, it is "hiding" at the right hand end)
- Put it after the first non-zero digit
- Count the number of digits that it would need to move to get back to its original position (if this is to the left, make it negative); put this as the power of 10.
- Multiply the results of steps 2 and 3 together.
Examples:
1234:
- No decimal point so hiding after the 4: "1234."
- 1.234
- to get decimal point back to original position it must move 3 digits right: 103
- 1.234 x 103
12.34:
- decimal point after the 2
- 1.234
- to get back to original position decimal point must move 1 digit right: 101
- 1.234 x 101
0.01234
- Decimal point after first zero
- 1.234 (first non-zero digit is the 1 - the leading zeros are removed)
- to get back to original position decimal point must move 2 digits left: 10-2
- 1.234 x 10-2.
How do you enter scientific notation into a calculator?
First of all, you have to have a scientific calculator, one that supports scientific notation. (As far as I know, all scientific calculators do.) The scientific calculator should have a special key labelled something like EXP. To input (for example) 2.3 million, you would type 2.3 EXP 6 (where EXP is short for "times 10 to the power...").
How do you express numbers in scientific notation?
In the number 123,000,000,000 The coefficient will be 1.23
To find the exponent count the number of places from the decimal to the end of the number.
In 123,000,000,000 there are 11 places. Therefore we write 123,000,000,000 as:
Exponents are often expressed using other notations. The number 123,000,000,000 can also be written as:
1.23E+11 or as 1.23 X 10^11
For small numbers we use a similar approach. Numbers less smaller than 1 will have a negative exponent. A millionth of a second is:
0.000001 sec. or 1.0E-6 or 1.0^-6
Very very small numbers as for example 0.00000078 = 7.8*10^-7 in scientific notation
How do you express 0.0763 in scientific notation?
Scientific Notation is a way of expressing a number as a value between 1 and 10 multiplied by a power of 10.
So, 0.0763 = 7.63 x 10-2
