Suppose you want to express the number N in base b (b > 1).
Assume, for the moment that N > 0. If N < 0 the method is the same, you just stick a minus sign in front. The reason for the assumption is that step one is not defined if N < 0. I would have had to define everything in terms of abs(n) and then disentangle it at the end.
The first step is to find logbN = log10N/log10b
this will be some real number k such that N = bk.
The next step is to find the largest integer, i which is less than or equal to k and then let j = k - i.
If k > 0 then i is the integer part of k and j is the fractional part, 0 ≤ j < 1.
If k < 0 then i is the integer before k and j is the positive increment to it. Again, 0 ≤ j < 1
[The key point here is that if, for example, k = -3.2 then i = -4 and j = +0.8]
Then N = bk = bi+j = bj+i = bj * bi
The final step is to calculate bj = a
and, since 0 ≤ j < 1 you have 0 ≤ bj < b
then N = a*bi is the scientific notation for N in base b.
It is: 7.0*10-9 when in scientific notation
It's probably in base ten because we use base ten for all our OTHER work in numbers as well. We learn to write numbers in base ten when in elementary school, and use base ten throughout our lives even if we aren't scientists or mathematicians or students or professionals who need to use scientific notation. So keeping scientific notation in base ten makes it easier for everyone to learn and read.
It is not. "Scientific notation" uses a base of 10. The correct notation would be 1.251 x 10^8
Something that is a billion starts with base 109. Therefore, the term in scientific notation is 7.0 x109
10 is the base in this case.
It is ten.
It is: 7.0*10-9 when in scientific notation
It's probably in base ten because we use base ten for all our OTHER work in numbers as well. We learn to write numbers in base ten when in elementary school, and use base ten throughout our lives even if we aren't scientists or mathematicians or students or professionals who need to use scientific notation. So keeping scientific notation in base ten makes it easier for everyone to learn and read.
It is not. "Scientific notation" uses a base of 10. The correct notation would be 1.251 x 10^8
No. 35 is exponential notation, (3 is the base of the exponent 5), but in scientific notation the base must be 10 and the exponent must be an integer. 100.1 is exponential notation but not sci. notation.
Something that is a billion starts with base 109. Therefore, the term in scientific notation is 7.0 x109
10 is the base in this case.
Shift a decimal place to the right, so the exponent for base 10 is -1. Then, the term in scientific notation is: 3.456789 x 10-1
Scientists have developed a shorter method to express very large numbers. This method is called scientific notation. Scientific Notation is based on powers of the base number 10.The number 123,000,000,000 in scientific notation is written as :
Scientific notation
Something that is a trillion starts off with this base 1012. Therefore, 3.65 trillion is 3.65 x 1012 in scientific notation.
Move 3 decimal places for 1652.0 and the exponent for base 10 is 3. Therefore, the term in scientific notation is 1.652 x 10³.