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To Convert to Scientific Notation From a Normal Number
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We can now give the rules for converting numbers between scientific notation and regular numbers...
To convert to scientific notation, from a normal number:
1. move the decimal as many places as needed so that the number is between 1 and 10 (not including 10)
2. multiply that number by ten to the power of however many places you moved the decimal, and make the power...
...negative if you
moved to the right.

Meaning you have
a small number.
...positive if you
moved to the left

Meaning you have
a big number.


Example 1: Change 3,960,000 into scientific notation

Here's all the ways to write 3,960,000 as a number times a power of 10 up to a power of 6. Only the last one is in scientific notation.
3,960,000 = 3,960,000 x 100 -> decimal moved 0 times to left
3,960,000 = 396,000 x 101 -> decimal moved 1 time to left
3,960,000 = 39,600 x 102 -> decimal moved 2 times to left
3,960,000 = 3960 x 103 -> decimal moved 3 times to left
3,960,000 = 396 x 104 -> decimal moved 4 times to left
3,960,000 = 39.6 x 105 -> decimal moved 5 times to left
3,960,000 = 3.96 x 106 -> decimal moved 6 times to left

This one is scientific notation because 3.96 is between 1 and 10.

Example 2: Change .00072 into scientific notation.
Here's all the ways to write .00072 as a number times a power of 10 down to a power
                                                                        of – 4. Only the last one is scientific notation.
Here's all the ways to write .00072 as a number times a power of 10 down to a power of -4. Only the last one is scientific notation.
.00072 = .00072 x 100 -> decimal moved 0 times to right
.00072 = .0072 x 10-1 -> decimal moved 1 time to right
.00072 = .072 x 10-2 -> decimal moved 2 times to right
.00072 = .72 x 10-3 -> decimal moved 3 times to right
.00072 = 7.2 x 10-4 -> decimal moved 4 times to right

This one is scientific notation because 7.2 is between 1 and 10.
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Writing Scientific Notation
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When The Coefficient is Not Between 1 and 10
 
   
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