How to find the quotient using scientific notation? 7.8x10^-1 over 3x10^-6

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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The required result is the quotient when 7.8*10^-1 is divided by 3*10^-6

(7.8*10^-1)/(3*10^-6)

=> 7.8*10^6/3*10

=> 2.6*10^5

The required quotient is 2.6*10^5

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll take each term at a time:

7.8 = 78/10

We'll use the negative power property to express 10^-1:

10^-1 = 1/10

We'll multiply 7.8 by 10^-1:

7.8*10^-1 = (78/10)*(1/10)

7.8*10^-1 = 78/100

We'll use the negative power property to express 10^-6:

10^-6 = 1/10^6

3*10^-6 = 3/10^6

We'll divide 78/100 by 3/10^6. We'll recall the fact that when dividing two fractions, the 1st fraction is multiplied by the 2nd inverted fraction:

7.8*10^-1/3*10^-6 = (78/10^2)*(10^6/3)

We'll simplify and we'll get:

(78/10^2)*(10^6/3) = [78*10^(6-2)]/3

[78*10^(6-2)]/3 = 26*10^4

The requested quotient is: (7.8*10^-1)/(3*10^-6)= 26*10^4

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