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)

Calculate the quotient below and give your answer in scientific notation.

`\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`

Calculate the product below and give your answer in scientific notation.

`\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`