write the scientific notation of 0.000002×0.0000003
Answers
Answer:
When numbers are very large or very small, you should write them in a short-hand form. For example, let's say you have a number like 560,000,000 or 0.0000003. Would you want to write those numbers over and over again? How can you simplify them? First of all, there is the way that the power of 10 works - that you have the following relations -
101 = 10 (anything to the power of 1 equals itself)
102 = 100
103 = 1000
104 = 10000
and so forth.
You'll notice how the power on the 10 equals the number of zeros after the 1. How do you write 560,000,000? You might notice that this number is also equal to 5.6 x 100,000,000, which can be written as 5.6 x 108. This format is known as scientific notation. What about numbers smaller than 10? How do you write those? Here's how -
100 = 1 (any number to the power of 0 = 1)
10-1 = 0.1
10-2 = 0.01
10-3 = 0.001
and so forth.
These aren't as easy as the others. In this case, the power on the 10 could represent how many places the decimal point is moved to the left of the 1. Now back to the original question: how do you write 0.0000003 using this? You might note that 0.0000003 is equal to 3 x 0.0000001, which is 3. x 10-7. You'll notice that in both cases, the decimal point is placed after the first non-zero number. This is the normal way that these numbers are written and it is also useful to use this method when writing similar numbers.
Let's try some more. How would you write the following numbers?
0.00045
345000
0.066
-0.000102
-53000
Check your answers here.
The next thing that you might have to do with numbers in scientific notation is to multiply or divide them. Generally this is pretty easy with a calculator. One of the things people don't know about their calculators is that there is usually a built in key that allows you to represent numbers in scientific notation in your calculator. The key is usually labeled with EE or Exp - what it actually is called will depend upon the type of calculator you have.
Let's go through an example of how you put a number into your calculator. Let's say you want to do the following problem -
4.5 x 10-5 x 3.3 x 106.
Here's what you do -
1. Put in the front part of the first number, 4.5 in this case.
2. Press the EE or Exp key. This usually causes a "00" or a "x10" to show up.
3. Enter the power on the 10, in this case -5. You don't want to use the subtraction key; use a key labeled ± or +/-. Don't put a "10" in since your calculator already has taken care of that.
4. Now press the multiply key.
5. Enter the second number, first the 3.3.
6. Press the EE or Exp key.
7. Put the power that is operating on the 10 in, which is 6 in this case.
8. Now press the equals or enter key to finish off the calculation.
If everything went all right, you should have gotten 148.5 (or 1.485 x 102, 1.485E2, or 1.485e2). Any way, that's the answer you should have gotten. If you didn't you should review the steps.
Here are some examples to try out - try to get the correct answer in each case
9.9 x 10-5 x 4.5 x 10-8
1.02 x 104 / 3.3 x 10-9
4.0 x 10-2 x 1.0 x 108
8.2 x 109 x 5.3 x 108
9.8 x 1019 + 4.2 x 10-9
Check your answers here.
=0.000002 × 0.0000003