Lesson 2

 

Adjusting the Decimal Place

Sometimes you have to adjust a number that already has an exponent to get it into proper scientific notation.

For example let's start with the number 64 times 10 to the third. It is not in proper scientific notation because the decimal place is not immediately to the right of the first non-zero number. It should be right after the 6. To get it there, it must be moved one place to the left. As the decimal moves one place to the left, the exponent must become one digit larger. Consequently, the number becomes 6.4 times 10 to the fourth.
64x103 = 64.x103 = 6.4x104
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You could break the process down into steps. Change the 64 into 6.4 times 10. Then 10 times 10 to the third becomes 10 to the fourth.
64x103 = (6.4x101) x 103 = 6.4x104

 

Next, we have .0032 times ten to the fifth. In this case, in order to get the decimal point in the proper position, right behind the 3, the decimal point has to be moved to the right three places. Then the exponent is reduced by 3, from 5 down to 2. So the number becomes 3.2 times 10 to the second.
0.0032x105 = 0.0032x105 = 3.2x102
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Notice that when you move the decimal point to the left, the exponent gets larger; and when you move the decimal point to the right, the exponent gets smaller.  The previous examples all had positive exponents.

When you are dealing with negative exponents, you must remember that the more negative the exponent, the smaller the number. For example negative 4 is less than negative 3. This is pointed out in the next examples.

Start with 0.015 times 10 to the negative 3. When you move the decimal two places to the right to get it behind the one, the value of the exponent has to go down by two. Since it is already at negative 3, going down makes it negative 5. So the number becomes 1.5 times 10 to the negative 5.
0.015x10-3 = 0.015x10-3 = 1.5x10-5
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Here is another example, 750 times 10 to the negative 8. Here we have to move the decimal two places to the left and make the exponent larger by 2. Starting with the exponent at negative 8, getting larger takes it up to negative 6. The value becomes 7.5 times 10 to the negative 6.
750x10-8 = 750.x10-8 = 7.5x10-6
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