To evaluate the energy of scientific notation, let"s begin with a straightforward example. Making use of nothing however a pencil and also piece of scrap paper, execute the adhering to operations:1. Add 5 and 3.2. Division 100 by 52, come the nearest tenth.3. Subtract 503 native 10300.4. Main point 34,074,000,000, 000,000,000,000,000 by 0.0000000000000000000000 000000000000000000000000 0000000000732.Having any type of trouble?
Chances are you to be breezing follow me pretty smoothly till you came to problem 4. Once numbers loss within a range that you can intuitively grasp, it"s enough to stand for them through the symbols you"ve known because kindergarten. Yet the variety of number one works v when trying out the Universe"s full scale is therefore overwhelming that a new method of representing them i do not care essential.
You are watching: 10 to the power of -6
Scientific notation is such a method, and also in scientific research it"s together imperative together elementary college multiplication tables. The general type of a number in scientific notation is:
N x 10x,
which in native reads: N times 10 raised to the power of x, whereby x is called the exponent, or power that 10. To transform an plain number to its scientific notation counterpart, here"s a two-step process:
1. Locate the decimal point of your number, and move it one of two people to the ideal or come the left, so that there is just one non-zero number to the left the it. This new number is your N.
2. Counting the number of spaces friend just had to move your decimal point. If you relocated to the left, climate each room adds 1 to x (where x starts at zero.) If you relocated to the right, then each room adds -1 come x.
EXAMPLE 1: 5,230,400.00For action 1, you need to relocate the decimal suggest 6 locations to the left. The number currently reads: 5.23040000, or 5.2304 (since any kind of trailing zeroes may be dropped.) for this reason 5.2304 is your worth of N.
See more: Which American Personally Took Part In The Invasion Of Cuba, Cuban Missile Crisis
For action 2, recall that you have actually moved 6 placess come the left, so that your worth of x = 6. So your number in clinical notation is: 5.2304x106, or "5.2304 times 10 to the 6th (power.)"
EXAMPLE 2: 0.00038This time, you move the decimal allude to the right, 4 spaces. N = 3.8 and also x = -4. So your number in scientific notation becomes: 3.8x10-4, or 3.8 times 10 to the negative-fourth (power.)
Once you have actually converted her number into scientific notation, friend will find that computations become much easier. Right here are 5 rules the numbers in scientific notation obey:
ADDITION and SUBTRACTION:
This one"s trickier. In the very first number being multiplied, 10 is elevated to the power of 5, while in the 2nd number, 10 is raised to the strength of 6. To add these two numbers, we must write castle both utilizing the exact same exponent. So we"ll require to change the type of among them. We"ll (arbitrarily) choose the an initial number, and adjust (4 x 105) come a kind with exponent 6 rather of 5. Remember that for every decimal transition to the left we add +1 to the exponent, and also for each change to the best we add -1. Due to the fact that we desire to add +1 come our exponent the 5, we move the decimal point once to the left, and also our number becomes: (0.4 x 106.)
currently both numbers have actually the very same exponent worth of 6. Including them, we find:
(Recall that increasing a number come the strength 1/2 is indistinguishable to acquisition the square root.)
RAISING to THE strength OF ZERO
One special case is worthy of being noted here: elevating a number to the strength of zero. You could think that anything raised to the strength of zero would be zero. However consider the trouble that that would cause:
Anything separated by itself is 1. In particular,(103)/(103) = 1.But (103)/(103) have the right to be to express as(103)(10-3),
and through the dominance of including and subtracting exponents, (103)(10-3) = 10(3-3)which = 100; therefore 100 must equal 1.