randRange( 1, 9 ) * Math.pow( 10, randRange( -5, 5 ) ) randRange( 1, 99 ) * Math.pow( 10, randRange( -5, 5 ) ) DENOMINATOR * QUOTIENT

Express this quotient in scientific notation: \Large{\frac{scientific( 3, NUMERATOR )} {scientific( 1, DENOMINATOR )}}

scientificMantissa( 2, QUOTIENT )  \times 10  scientificExponent( QUOTIENT )

Start by collecting like terms together.

= \Large{\frac{scientificMantissa( 3, NUMERATOR )} {scientificMantissa( 1, DENOMINATOR )}} \times\Large{\frac{10^{scientificExponent( NUMERATOR )}} {10^{scientificExponent( DENOMINATOR )}}}

Then divide each term seperately. When dividing exponents with the same base, subtract their powers.

= roundTo( 2, scientificMantissa( 3, NUMERATOR ) / scientificMantissa( 1, DENOMINATOR ) ).toFixed( 2 ) \times 10^{scientificExponent( NUMERATOR )\,-\,scientificExponent( DENOMINATOR )}

= roundTo( 2, scientificMantissa( 3, NUMERATOR ) / scientificMantissa( 1, DENOMINATOR ) ).toFixed( 2 ) \times 10^{scientificExponent( NUMERATOR ) - scientificExponent( DENOMINATOR )}

To write the answer correctly in scientific notation, the first number needs to be between 1 and 10. In this case, we need to move the decimal one position to the right without changing the value of our answer.

\qquadWe can use the fact that roundTo( 2, scientificMantissa( 3, NUMERATOR ) / scientificMantissa( 1, DENOMINATOR ) ).toFixed( 2 ) is the same as scientificMantissa( 2, QUOTIENT ) \div 10, or scientificMantissa( 2, QUOTIENT ) \times 10^{-1}.

 = \color{BLUE}{scientificMantissa( 2, QUOTIENT ) \times 10^{-1}} \times 10^{scientificExponent( NUMERATOR ) - scientificExponent( DENOMINATOR )} 

= scientific( 2, QUOTIENT )

Express this product in scientific notation: (scientific( 2, QUOTIENT ))\times (scientific( 2, DENOMINATOR ))

scientificMantissa( 3, NUMERATOR )  \times 10  scientificExponent( NUMERATOR )

Start by collecting like terms together.

= (scientificMantissa( 2, QUOTIENT )\times scientificMantissa( 2, DENOMINATOR )) \times (10^{scientificExponent( QUOTIENT )}\times 10^{scientificExponent( DENOMINATOR )})

When multiplying exponents with the same base, add the powers together.

= roundTo( 1, scientificMantissa( 2, QUOTIENT ) * scientificMantissa( 1, DENOMINATOR ) ).toFixed( 1 ) \times 10^{scientificExponent( QUOTIENT )\,+\,scientificExponent( DENOMINATOR )}

= roundTo( 1, scientificMantissa( 2, QUOTIENT ) * scientificMantissa( 1, DENOMINATOR ) ).toFixed( 1 ) \times 10^{scientificExponent( QUOTIENT ) + scientificExponent( DENOMINATOR )}

To write the answer correctly in scientific notation, the first number needs to be between 1 and 10. In this case, we need to move the decimal one position to the left without changing the value of our answer.

\qquadWe can use the fact that roundTo( 1, scientificMantissa( 2, QUOTIENT ) * scientificMantissa( 1, DENOMINATOR ) ).toFixed( 1 ) is the same as scientificMantissa( 3, NUMERATOR ) \times 10.

 = \color{BLUE}{scientificMantissa( 3, NUMERATOR ) \times 10} \times 10^{scientificExponent( QUOTIENT ) + scientificExponent( DENOMINATOR )} 

= scientific( 3, NUMERATOR )