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$F=(6.674\times 10^{-11})(80)(7.4\times 10^{22})/(3.8\times 10^{8})^{2}$

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Divide numbers written in scientific notation

Full solution

Q.

F=(6.674\times 10^{-11})(80)(7.4\times 10^{22})/(3.8\times 10^{8})^{2}

Group Constants and Powers: Group the constants and the power of $10$ terms separately. $\newline$ $F = (6.674 \times 10^{-11}) \times 80 \times (7.4 \times 10^{22}) / (3.8 \times 10^{8})^{2}$
Calculate Numerator: Calculate the numerator by multiplying the constants and the powers of $10$ . $\text{Numerator} = (6.674 \times 80 \times 7.4) \times (10^{-11} \times 10^{22})$
Calculate Constants: Calculate the constants in the numerator. $\newline$ Constants = $6.674 \times 80 \times 7.4$
Combine Powers: Combine the powers of $10$ in the numerator. $\newline$ Powers of $10 = 10^{-11} \times 10^{22} = 10^{22 - 11} = 10^{11}$
Calculate Denominator: Calculate the denominator by squaring the power of $10$ term. $\newline$ Denominator = $(3.8 \times 10^8)^2$
Square Constant: Square the constant and the power of $10$ separately in the denominator. $\newline$ Denominator = $(3.8^2) \times (10^8)^2$
Combine Powers: Combine the powers of $10$ in the denominator. $\newline$ Powers of $10$ = $(10^8)^2 = 10^{8 \times 2} = 10^{16}$
Divide Numerator: Now divide the numerator by the denominator. $\newline$ $F = \frac{\text{Constants} \times 10^{11}}{3.8^2 \times 10^{16}}$
Calculate Constant: Calculate the constant $3.8$ squared. $\newline$ $3.8^2 = 14.44$
Divide Separately: Divide the constants and the powers of $10$ separately. $\newline$ $F = (\text{Constants} / 14.44) \times (10^{11} / 10^{16})$
Combine Powers: Combine the powers of $10$ in the final step. $\newline$ Powers of $10 = 10^{11} / 10^{16} = 10^{11 - 16} = 10^{-5}$
Calculate Final Constant: Calculate the final constant value. $\newline$ Final Constants = $\frac{\text{Constants}}{14.44}$

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