# Khan/khan-exercises

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 Multiplying and dividing scientific notation
randRange(1, 9) * Math.pow(10, randRange(-5, 5)) randRange(1, 99) * Math.pow(10, randRange(-5, 5)) DENOMINATOR * QUOTIENT scientific(2, DENOMINATOR) scientific(2, QUOTIENT) scientific(3, NUMERATOR) localeToFixed(scientificMantissa(2, DENOMINATOR), 1) localeToFixed(scientificMantissa(2, QUOTIENT), 1) localeToFixed(scientificMantissa(3, NUMERATOR), 2) localeToFixed(roundTo(2, MANTISSA_3 / MANTISSA_1), 2) localeToFixed(roundTo(1, MANTISSA_1 * MANTISSA_2), 1) scientificExponent(DENOMINATOR) scientificExponent(QUOTIENT) scientificExponent(NUMERATOR)

\large{\dfrac{SCIENTIFIC_3}{SCIENTIFIC_1}} =\ ?

scientificMantissa(2, QUOTIENT) \times 10 EXPONENT_2

Start by collecting the significands and exponents.

\large{\dfrac {\blue{MANTISSA_3} \times \pink{10^{EXPONENT_3}}} {\blue{MANTISSA_1} \times \pink{10^{EXPONENT_1}}} = \blue{\dfrac{MANTISSA_3}{MANTISSA_1}} \times \pink{\dfrac{10^{EXPONENT_3}}{10^{EXPONENT_1}}}}

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

= \blue{MANTISSA_DIV} \times \pink{10^{EXPONENT_3 \,-\, EXPONENT_1}}

= \blue{MANTISSA_DIV} \times \pink{10^{EXPONENT_3 - EXPONENT_1}}

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.

We can use the fact that \blue{MANTISSA_DIV} is the same as \green{MANTISSA_2 \div 10}, or \green{MANTISSA_2 \times 10^{-1}}.

= \green{MANTISSA_2 \times 10^{-1}} \times \pink{10^{EXPONENT_3 - EXPONENT_1}}

= MANTISSA_2 \times 10^{\green{-1} + \pink{EXPONENT_3 - EXPONENT_1}}

= SCIENTIFIC_2

\large{\left(SCIENTIFIC_2 \right) \times \left(SCIENTIFIC_1 \right) =\ ?}

scientificMantissa(3, NUMERATOR) \times 10 EXPONENT_3

Start by collecting the significands and exponents.

(\blue{MANTISSA_2} \times \pink{10^{EXPONENT_2}}) \times (\blue{MANTISSA_1} \times \pink{10^{EXPONENT_1}}) = (\blue{MANTISSA_2} \times \blue{MANTISSA_1}) \times (\pink{10^{EXPONENT_2}} \times \pink{10^{EXPONENT_1}})

Then multiply each term separately. When multiplying exponents with the same base, add the powers together.

= \blue{MANTISSA_MUL} \times \pink{10^{EXPONENT_2 \,+\, EXPONENT_1}}

= \blue{MANTISSA_MUL} \times \pink{10^{EXPONENT_2 + EXPONENT_1}}

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.

We can use the fact that \blue{MANTISSA_MUL} is the same as \green{MANTISSA_3 \times 10} or \green{MANTISSA_3 \times 10^{1}}.

= \green{MANTISSA_3 \times 10^{1}} \times \pink{10^{EXPONENT_2 + EXPONENT_1}}

= MANTISSA_3 \times 10^{\green{1} + \pink{EXPONENT_2 + EXPONENT_1}}

= SCIENTIFIC_3