Question 358669
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54.0= 

A.  Write the leftmost non-zero digit followed by a decimal

                   5.

B.  Write all the digits that follow it after the decimal, unless the decimal
    is not showing, and there are trailing zeros.  If the decimal is showing
    then include all trailing zeros.

                   Here the decimal is showing in the original, so we include
                   the trailing zero
 
                   5.40


C.  Write × 10 after that

                   5.40 × 10

D.  Count the number of decimal places the original number is to the
    right or left of the decimal you now have.  If it is to the right,
    the exponent of 10 is that number taken positive.  If it is   
    to the left it is taken negative.

                   The decimal of 54.0 is 1 place to the right of the
                   decimal in 5.40, so we give the 10 the exponent 1
                   taken positive, so the answer is 

                   5.40 × 10<sup>1</sup> 

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4567=

A.  Write the leftmost non-zero digit followed by a decimal

                   4.

B.  Write all the digits that follow it after the decimal, unless the decimal
    is not showing, and there are trailing zeros.  If the decimal is showing
    then include all trailing zeros.

                   The decimal was not showing so it was understood at the
                   end as 4567.  There were no trailing zeros.
                   
                   4.567


C.  Write × 10 after that

                   4.567 × 10

D.  Count the number of decimal places the original number is to the
    right or left of the decimal you now have.  If it is to the right,
    the exponent of 10 is that number taken positive.  If it is   
    to the left it is taken negative.

                   The decimal of 4567 is understood to be at the end
                   so it is actually 4567. which is 3 places to the 
                   right of the decimal in 4.567, so we give the 10 the
                   exponent 3 taken positive, so the answer is 

                   4.567 × 10<sup>3</sup> 

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0.345000=

A.  Write the leftmost non-zero digit followed by a decimal

                   3.

B.  Write all the digits that follow it after the decimal, unless the decimal
    is not showing, and there are trailing zeros.  If the decimal is showing
    then include all trailing zeros.


                   The decimal is showing in the original, so we
                   retain all the trailing zeros.

                   3.45000


C.  Write × 10 after that

                   3.45000 × 10

D.  Count the number of decimal places the original number is to the
    right or left of the decimal you now have.  If it is to the right,
    the exponent of 10 is that number taken positive.  If it is   
    to the left it is taken negative.

                   The decimal of 0.345000 is 1 place to the left of the
                   decimal in 3.45000, so we give the 10 the exponent -1
                   (taken negative because it's left), so the answer is 

                   3.45000 × 10<sup>-1</sup> 

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10000000=

A.  Write the leftmost non-zero digit followed by a decimal

                   1.



B.  Write all the digits that follow it after the decimal, unless the decimal
    is not showing, and there are trailing zeros.  If the decimal is showing
    then include all trailing zeros.


                   The decimal is not showing so we do not write any trailing
                   zeros, so we still have only

                   1.


C.  Write × 10 after that

                   1. × 10

D.  Count the number of decimal places the original number is to the
    right or left of the decimal you now have.  If it is to the right,
    the exponent of 10 is that number taken positive.  If it is   
    to the left it is taken negative.

                   The decimal of 10000000 is understood at the right end
                   as 10000000. which is 7 places to the right of the
                   decimal in 1., so we give the 10 the exponent 7
                   taken positive, so the answer is 

                   1 × 10<sup>7</sup> 

                   We do not write the decimal at the right end of just 1
                   digit. 
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0.009078

A.  Write the leftmost non-zero digit followed by a decimal

                   9.

B.  Write all the digits that follow it after the decimal, unless the decimal
    is not showing, and there are trailing zeros.  If the decimal is showing
    then include all trailing zeros.

                   9.078


C.  Write × 10 after that

                   9.078 × 10

D.  Count the number of decimal places the original number is to the
    right or left of the decimal you now have.  If it is to the right,
    the exponent of 10 is that number taken positive.  If it is   
    to the left it is taken negative.

                   The decimal of 0.009078 is 3 places to the left of the
                   decimal in 9.078, so we give the 10 the exponent -3
                   (taken negative because it's left), so the answer is 

                   9.078 × 10<sup>-3</sup>

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2.3=

A.  Write the leftmost non-zero digit followed by a decimal

                   2.

B.  Write all the digits that follow it after the decimal, unless the decimal
    is not showing, and there are trailing zeros.  If the decimal is showing
    then include any trailing zeros.                  
 
                   2.3


C.  Write × 10 after that

                   2.3 × 10

D.  Count the number of decimal places the original number is to the
    right or left of the decimal you now have.  If it is to the right,
    the exponent of 10 is that number taken positive.  If it is   
    to the left it is taken negative.

                   The decimal of 2.3 is 0 places to the right or left
                   of the decimal in 2.3, so we give the 10 the exponent 0
                   so the answer is 

                   2.3 × 10<sup>0</sup>

Edwin</pre>