Mathematics

Question

What's the scientific notation of 4,890,000? Please show work because I don't really understand how to do this type of math stuff ;-;

1 Answer

  • The correct answer:
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    The number:  "4,890,000" ; written in "scientific notation", is:
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    4.89 * 10 ⁶ .
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    To write a number using "scientific notation", one:
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    1)  Looks at the entire number, and consider the "string of sequential digits" that are either precede OR any digit or trailing digits of "zero" --- if any exist.
    Regardless if any exist, one considers, for a moment, that "string of digits", or "single digit, for that member" as a number, in and of itself.  Considering this value as a number, one write the first digit in that number.  If there are more than one digit in this "number", one writes a decimal place, and then writes ALL THE DIGITS THAT FOLLOW (if there are any), in sequential order, unit the last non-zero integer is reached.  Then, one writes a multiplication sign, and then the number 10 (with an appropriate assigned to the "10", which may be: "1", or a "negative number", or a positive number.  To find out the correct number to write, one refers to the ORIGINAL NUMBER; then one looks at what one has written down—and where the decimal point has been written at the number written down.  One matches this "decimal point" place to the ORIGINAL number, and then counts the FULL NUMBER OF TENS PLACES to the right, or left, until the ENTIRE number is complete (this would include any "trailing zeros" to the right; OR to the left; but not BOTH.  If to the left, one would count UP TO AND INCLUDING the decimal point, but NOT the number "0" that is BEFORE the decimal point.   If to the left, the exponent would be a "negative number"; then number of spaces to the LEFT.  If to the right, the exponent would be the number of spaces to the RIGHT (including the trailing zeros).
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    So, for this problem.
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    4.89 * 10
     .  (That is, 4.89* 10^6 ; because we have the whole number, "4";  then we write the "decimal point". Then we write the sequential digits: "89"; 
    and then:  we write:
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       "   *  10
    ⁶   " ;
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         since, after the number "4", we count the 8, then the 9, (which is already TWO (2) places, then all the remaining digits (the remaining FOUR (4) zeros), until the end of the number is reached.
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        Additional note:   As a matter of technicality:  Consider the following:
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    How would we write: "49" ; in scientific notation?
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    Answer:  In reality, we probably would not write such a small number in scientific notation, but we could if we wanted.  The answer would be:
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            4.9  *  10¹ .
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     How would we write:  "-49" ; in scientific notation?
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    Answer: Again, in reality we probably wouldn't, because it wouldn't be practical.   But the answer is:  -4.9 * 10
    ¹ .
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    What is:  "0.49" in scientific notation?  Answer:  4.9 * 10
    ⁻¹  
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    Similar to our problem:
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    What is: "0.0000489" in scientific notation?  
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    Answer:  4.89 * 10⁻⁵  (that is, 4.89 * 10^(-5) ).  Since we write down the "whole number integer, plus a decimal, then we would count the number of spaces BACK FROM (in this case) the decimal.
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    What about "0.0000489002" in scientific notation?
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    Answer:  4.89002 * 10⁻⁵ (that is:  4.89002 * 10^(-5) ).
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    What about:  0.0004890000 ?
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    Answer:  Though often prone to debate by some, we would still be on the safe side and write as: 
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      4.890000 * 10 ⁻⁴ .
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    How to write: "5" in scientific notation? Answer: 5 * 10⁰ .
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     (since anything to the "0th" power = 1 ;
     and as such, 5 = 5 * 10⁰ = 5 * 1 = 5).
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    Hope that this lengthy explanation is of help!
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