can anyone explain scientific notation?

Question

how do you wrie 6,000,000,000,000,000,000,000 in scientific notation? Also, can you explain how to convert numbers into scientific notation in general?
thanks

Answer 1

Since there are 21 zeroes

6 x 10^21

0.0003 would be written as

3 x 10^(-4)

which is the same as 3/(10000).
.

Answer 2

You can think of scientific notation as a way of writing numbers in a manner that is not only very convenient for many calculations, but that also enables you to "size up" their value in general order-of-magnitude terms that might be more difficult if you just wrote out all the zeros there might be every time.

Thus the number of particles in the observable universe,
something of the order of 10^78 or more, would take 78 or more decimal places to write out in "regular" (non-scientific) notation. At the opposite end of the scale, the typical size of an atom (10^(-15)m) would take an awful lot (14) of zeros after the decimal point, before the first non-zero digit would appear.

Your requested number, 6,000,000,000,000,000,000,000, is
6 x 10^21 or 6.0 x 10^21, if you prefer. In this case (but ONLY because the number starts with just one significant, non-zero digit --- see below), the power of 10 is 21 because "that's the number of zeros." (I'll explain below why you can't always just "count the zeros" in general.)

The leading part of the number is always written as either a whole number or a decimal number 'n' lying in the range between exactly 1 and 9.9999... . (The upper limit is as close to 10 as you like, but not equal to 10. If it were 10, you'd be back at a leading number of 1 again.)

I'll now divide up the discussion of the exponent of 10 into two cases:

CASE A. The overall number is LARGER THAN 1.

To get the number of zeros for a general number, consider the number 1,234, 567, say. That's 1.234567 x 1,000,000. Just as 10 is 10^1 and 100 is 10^2 (though that would apparently be news to an earlier responder!), the exponent of 10 for 1,000,000 is the number of zeros, that is 6. So

1,234,567 = 1.234567 x 10^6.

[ Note that the advice to just "count the zeros" is too loose when the number ISN'T a pure power of 10! What you count is the number of IMPLIED zeros were you to put some number abcdefg... (each letter representing a digit) into the form

a.bcdefg... x some power of 10.

In practical terms, this means that you IGNORE the leading digit in any such number, then count all of the spaces lying between IT and the decimal point. THAT will give you the exponent of 10. ]

CASE B. The overall number is LESS THAN 1.

Now consider decimal numbers that are smaller than 1. The quantity 1/10 = 0.1, 1/10^2 = 1/100 = 0.01, 1/10^3 = 1/1000 = 0.001 etc. You'll notice that the rule for such numbers is SUBTLY DIFFERENT than for numbers greater than 1. Here, the number of zeros in the decimal expression is ONE LESS THAN the number of zeros in the power of 10 dividing the 1.

Consider the effect of that on writing the number 0.001234567 in scientific notation.

That number is 1.234567 x 0.001, and I've shown above that 0.001 means 1/1000 or 10^(-3). This is an example of the general rule for numbers less than 1:

Count the number of zeros, 'z' beween the decimal point and the first NON-ZERO digit (In the example just given, z = 2.) Add 1 to z; here, z + 1 = 3. Then your power of 10 is - (z + 1); here, that's - 3.

One more example. Consider 0.0678. There is just 1 zero; add 1 to 1, giving 2; the exponent will then be - 2; so it's 6.78 x 10^(-2).

C. A PRACTICAL SUMMARY!

If you've read and understood the principles explained above, there is a slightly more practical and efficient way of finding the power of 10 which corresponds to those principles:

For case A. Write out the full number as a regular decimal, say it's abcdefghi.jkl... . Take the decimal point and IMAGINE moving it LEFT until it's just AFTER the leading digit 'a.' The number of places it had to be moved (in this case, 8) is the power of 10. The number is a.bcdefghijkl... x 10^8.

For case B. How about 0.0000rstuv... ? Move the decimal point to the RIGHT until it's immediately after the leading non-zero digit 'r.' How many places did it move?(5, in this case.) The NEGATIVE of that number (- 5) is the needed power of 10; this number is r.stuv... x 10^(- 5).

It may seem a bit confusing at first, but like everything else in mathematics, with practice you'll become much more comfortable with it.

Good luck!

Live long and prosper.

Answer 3

In scientific notation, a number such as:
6235.4172
would be written
6.2354172 * 10^3 or 6.2354172 E 3.
The number is written with one digit to the left of the decimal point, and the power (3) of 10 indicates how many places the decimal point has to be moved to the right.
Your number is 6 * 10^21 or 6 E 21.

For small numbers such as 0.000 8216, the scientific form is
8.216 *10^(-4) or 8.216 E -4.
Again, you write one digit to the left of the decimal point, and the power of ten (because it is negative) indicates that the decimal point has to be moved left by 4 places.

The advantage of scientific notation is that you can instantly tell which is larger of 8.3 * 10^15 and 3.1 * 10^16, whereas given two numbers such as 8300000000000000 and 31000000000000000, the answer is not so obvious until you have counted the zeros.

Answer 4

well that would be 6 x 10^21. Basically Scientific Notation is based on powers of the base number 10.

The number 123,000,000,000 in scientific notation is written as : 1.23 x 10^11
The first number 1.23 is called the coefficient. It must be greater than or equal to 1 and less than 10.
The second number is called the base . It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1.23 x 1011 the number 11 is referred to as the exponent or power of ten.
To write a number in scientific notation:
Put the decimal after the first digit and drop the zeroes.
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: 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 1.0 x 10^-6

Answer 5

Scientific notation is a shorthand for writing really long numbers (like the one above). 6,000,000,000,000,000,000,000 = 6 x 10^21 (or 6 times 10 to the power 21).

The easiest way to convert to scientific notation is count the number of zeros after your first digit (that is the exponent)

Other examples:

5,213,652,005,323 = 5.213 x 10^12
1.7654 x 10^6 = 1,765,400

Answer 6

Yes, scientific notation is written such that the number (the ordinate, as I recall) is between -9.999... and 9.9999 and then multiplied by a power of 10. So 105 would be written as 1.05 X 10^1. On the other hand, 0.01 would be written as 1.0 * 10^-2

In general, just count how many places you have to move the decimal place to the left or the right, and then move it there and multiply the resulting number by ten to the nth power, where n is the number you've moved left or right. If you move left, then n is a positive number; if you move right, then it's a negative numbr. In your case you would write 6.00 x 10^21

Answer 7

count the number of zeros
answer : 6 x 10^21

Answer 8

DEFINE
to express some thing in scientific way.(6 '21)