Question 189667
<font size = 8 color = "red"><b>Edwin's solution:</b></font>
<pre><font size = 4><b>
Rules for changing a number from ordinary notation to scientific notation.

1. Locate the decimal point.  If none is showing place the decimal
   point on the right end.

25000000000000 has no decimal showing so we put
one on the right end, like this 

25000000000000.

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23420000 has no decimal showing so we put
one on the right end, like this 23420000.

0.000000586 shows its decimal.

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0.00000000000000000000000000167 shows its decimal.

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2. Starting at the far left find the first digit that isn't a zero. Put
a red decimal just to the right of that digit.  (You can choose another
color, or just make a different looking decimal there, maybe a little
cross mark or something, or you can use a pencil to write one decimal
and a pen to write the other one.  But I'll use a red decimal here)

25000000000000.  The digit 2 is the first digit that isn't a zero.
So we put a red decimal after that 2, like this:

2<font color = "red">.</font>5000000000000.

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23420000. The digit 2 is the first digit that isn't a zero.
So we put a red decimal after that 2, like this:

2<font color="red">.</font>3420000.

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0.000000586  The digit 5 is the first digit that isn't a zero.
So we put a red decimal after that 5, like this:
0.0000005<font color="red">.</font>86

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0.00000000000000000000000000167  The digit 1 is the first digit
that isn't a zero. So we put a red decimal just to the right of 
that 1, like this:
0.000000000000000000000000001<font color="red">.</font>67    

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3.  Count the number of digits between the black decimal and the
red decimal, and that will be the magnitude of the exponent of 10.

2<font color = "red">.</font>5000000000000.  There are 13 digits
between the black and red decimals. So the magnitude of the exponent
of 10 is 13

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2<font color="red">.</font>3420000.  There are 7 digits between the
black and red decimals. So the magnitude of the exponent
of 10 is 7

0.0000005<font color="red">.</font>86  There are 7 digits between the
black and red decimals. So the magnitude of the exponent
of 10 is 7.

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0.000000000000000000000000001<font color="red">.</font>67  There are 27
digits between the black and red decimals. So the magnitude of the exponent
of 10 is 27

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4. Now we determine whether the exponent is positive or negative.
If the black decimal is on the right of the red decimal, the exponent
of 10 is positive.
If the red decimal is on the right of the black decimsl, the exponent
of 10 is negative.

2<font color = "red">.</font>5000000000000.  The black decimal is 
right of the red decimal so the exponent of 10 is positive, and is
therefore +13  

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2<font color="red">.</font>3420000. The black decimal is 
right of the red decimal so the exponent of 10 is positive, and is
therefore +7  

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0.0000005<font color="red">.</font>86  The red decimal is 
right of the black decimal so the exponent of 10 is negative, and is
therefore -7  

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0.000000000000000000000000001<font color="red">.</font>67  The red decimal is 
right of the black decimal so the exponent of 10 is negative, and is
therefore -27. 

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5. Erase the black decimal and trim any leading or trailing zeros.

2<font color = "red">.</font>5000000000000. 

We erase the black decimal at the end

2<font color = "red">.</font>5000000000000 

Now we trim off all the trailing zeros:

2<font color = "red">.</font>5

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2<font color="red">.</font>3420000.

We erase the black decimal at the end

2<font color="red">.</font>3420000

Now we trim off all the trailing zeros:

2<font color="red">.</font>342

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0.0000005<font color="red">.</font>86

We erase the black decimal:

00000005<font color="red">.</font>86

Now we trim off all the leading zeros:

5<font color="red">.</font>86

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0.000000000000000000000000001<font color="red">.</font>67

We erase the black decimal:

0000000000000000000000000001<font color="red">.</font>67

Now we trim off all the leading zeros:

1<font color="red">.</font>67

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6. Finally we put " ×10<sup>EXPONENT OF 10</sup> " after it:

2<font color = "red">.</font>5 × 10<sup>13</sup>

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2<font color="red">.</font>342 × 10<sup>7</sup>

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5<font color="red">.</font>86 × 10<sup>-7</sup>

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1<font color="red">.</font>67 × 10<sup>-27</sup>

Edwin</pre>