When do we use scientific notation?

Question

help plzzz :pp

Answer 1

Hi,

Hope You and family are fine.


Scientific notation is usually used to express numbers that are either very very large, or very very small. It's a way of writing these numbers so that they don't take up a lot of space.

A number written in scientific notation is made up of two parts, a
decimal part, and a power of 10. For example, 2.1 x 10^6 is a number written in scientific notation. The 2.1 is the decimal part, and the 10^6 is the power of ten (the ^ symbol here means that the 6 is the exponent).

Numbers in scientific notation are really multiplication expressions.

We would read the above number as "2.1 times 10 to the sixth." Since 10^6 is 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000, then 2.1 times this is 2,100,000.


Why Use Scientific Notation?

Scientific Notation was developed in order to easily represent numbers that are either very large or very small. Here are two examples of large and small numbers. They are expressed in decimal form instead of scientific notation to help illustrate the problem:


The Andromeda Galaxy (the closest one to our Milky Way galaxy) contains at least 200,000,000,000 stars.

On the other hand, the weight of an alpha particle, which is emitted in the radioactive decay of Plutonium-239, is
0.000,000,000,000,000,000,000,000,006,645 kilograms.

As you can see, it could get tedious writing out those numbers repeatedly. So, a system was developed to help represent these numbers in a way that was easy to read and understand: Scientific Notation.


What is Scientific Notation?

Using one of the above examples, the number of stars in the Adromeda Galaxy can be written as:

2.0 x 100,000,000,000

It is that large number, 100,000,000,000 which cause the problem. But that is just a multiple of ten. In fact it is ten times itself eleven times:

10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 100,000,000,000

A more convenient way of writing 100,000,000,000 is 1011. The small number to the right of the ten is called the "exponent," or the "power of ten." It represents the number of zeros that follow the 1.

Though we think of zero as having no value, zeroes can make a number much bigger or smaller. Think about the difference between 10 dollars and 100 dollars. Any one who has balanced a checkbook knows that one zero can make a big difference in the value of the number. In the same way, 0.1 (one-tenth) of the US military budget is much more than 0.01 (one-hundredth) of the budget. (Though either one is probably more money than most of us will ever see in our checkbooks!)

So we would write 200,000,000,000 in scientific notation as:

2.0 x 1011

This number is read as follows: "two point zero times ten to the eleventh."


How Does Scientific Notation Work?

As we said above, the exponent refers to the number of zeros that follow the 1. So:

101 = 10;
102 = 100;
103 = 1,000,
and so on.

Similarly, 100 = 1, since the zero exponent means that no zeros follow the 1.

Negative exponents indicate negative powers of 10, which are expressed as fractions with 1 in the numerator (on top) and the power of 10 in the denominator (on the bottom).

So:

10-1 = 1/10;
10-2 = 1/100;
10-3 = 1/1,000,
and so on.

This allows us to express other small numbers this way. For example:

2.5 x 10-3 =
2.5 x 1/1,000 =
0.0025

Every number can be expressed in Scientific Notation. In our first example, 200,000,000,000 should be written as 2.0 x 1011. In theory, it can be written as 20 x 1010, but by convention the number is usually written as 2.0 x 1011 so that the lead number is less than 10, followed by as many decimal places as necessary.

It is easy to see that all the variations above are just different ways to represent the same number:

200,000,000,000 =
20 x 1010 (20 x 10,000,000,000)
2.0 x 1011 (2.0 x 100,000,000,000)
.2 x 1012 (.2 x 1,000,000,000,000)


This illustrates another way to think about Scientific Notation: the exponent will tell you how the decimal point moves; a positive exponent moves the decimal point to the right, and a negative one moves it to the left. So for example:

4.0 x 102 =
400 (2 places to the right of 4);
while
4.0 x 10-2 =
0.04 (2 places to the left of 4).

Note that Scientific Notation is also sometimes expressed as E (for exponent), as in 4 E 2 (meaning 4.0 x 10 raised to 2). Similarly 4 E -2 means 4 times 10 raised to -2, or = 4 x 10-2 = 0.04. This method of expression makes it easier to type in scientific notation.

Sometimes the advantage of scientific notation is not immediately obvious. A number like 340 is much easier to read in decimal form than in scientific notation:

340 or 3.4 x 102?
What about the number 380,000? At the end of 1994 the Department of Energy's (DOE) inventory of high level radioactive waste was approximately 378,400 cubic meters.


378,400 or 3.784 x 105?

The number 378,400 is also small enough to be readable. There are two reasons for expressing 378,400 in scientific notation rather than decimal form:

1) Computation: Scientific Notation makes adding, subtracting, multiplying and dividing numbers much simpler.



Hope this can help.

Take care,

Warm Regards,

Tanvir.

Answer 2

For very large numbers and extrememly small ones, these numbers can be placed in scientific notation in order to express them in a more concise form.

In addition, numbers placed in this notation can be used in a computation with far greater ease. This last advantage was more practical before the advent of calculators and their abundance.

In scientific fields, scientific notation is still used.

Answer 3

It is a standardized form of writing numbers such that the significant portion is reduced to a decimal value x, such that

-10 < x < 10

followed by a suitable multiple of 10.


For example,

61423 = 6.1423 x 10^4

0.0032 = 3.2 x 10^-3

-585.634 = -5.85634 x 10^2


The advantage is that all numbers, from very small to very larger numbers may be represented in a consistent form and be manipulated with clarity.

Answer 4

It is used mainly in the scientific community for very large and very small numbers, thus the name "scientific" notation.

Answer 5

To avoid writing or describing huge numbers greater than 1 x 10^3

Answer 6

let's say you wanna calculate the distant between earth and your Alien friend's home planet which came out to be
256,000,000,000,000,000,000 miles away ... :)

Scientific notation makes life easier ...
256 * 10^18

Easy enough .. right?

Answer 7

Thats easy man. To shorten long numbers. For example the "the height of Zeta Zeroes is 1.405 X 10^100^1000^386. Try writng that on a pieace of paper!!!!

Answer 8

This Site Might Help You.

RE:
When do we use scientific notation?
help plzzz :pp

Answer 9

Anytime you're dealing with scientific calculations. It makes multiplication and division **so** much easier. And normalizing before you add or subtract just amounts to shifting the decimal point right or left as required.


Doug

Answer 10

When using very large or very small numbers.