Calculate the quotient below and give your answer in scientific notation.
\large{\dfrac{SCIENTIFIC_3}{SCIENTIFIC_1}} =\ ?
\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) =\ ?}
\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