# Simplifying an arithmetic expression written using scientific notation.

• Oct 25th 2009, 03:19 PM
Simplifying an arithmetic expression written using scientific notation.
Hey, so. I need a problem worked out that uses Newton's gravitational constant.(If you dont want to read this, skip to the problem below) And, I have to present it to the class tommorrow.. I can punch it into a calculator just fine and do it when the exponets are gone (the problem is in scientific notation) BUT.. Since it will be explained to the class on a board, I want to leave the problem in scientific notation until the very end. I know the answer. N= 686. But I keep getting a different answer. Very frustrating.Im sure Im just making a small error. Anyway Problem is:

(6.673 x 10-11 N m2/kg2) x (5.98 x 1024 kg ) x (70 kg)
__________________________________________________
(6.38 x 10^6 m)^2
Whats used is Gravitation constant times mass of one times mass of two over distance squared.
So yeah, theres a way to multiply/divide and keep it in scientific notation, can someone please show a step by step how-to? Much appreciated.thanks.

• Oct 26th 2009, 12:05 AM
earboth
Quote:

Hey, so. I need a problem worked out that uses Newton's gravitational constant.(If you dont want to read this, skip to the problem below) And, I have to present it to the class tommorrow.. I can punch it into a calculator just fine and do it when the exponets are gone (the problem is in scientific notation) BUT.. Since it will be explained to the class on a board, I want to leave the problem in scientific notation until the very end. I know the answer. N= 686. But I keep getting a different answer. Very frustrating.Im sure Im just making a small error. Anyway Problem is:

(6.673 x 10-11 N m2/kg2) x (5.98 x 1024 kg ) x (70 kg)
__________________________________________________
(6.38 x 10^6 m)^2
Whats used is Gravitation constant times mass of one times mass of two over distance squared.
So yeah, theres a way to multiply/divide and keep it in scientific notation, can someone please show a step by step how-to? Much appreciated.thanks.

I'm not sure that I understand what you are asking ... (Thinking)

To simplify the given term you can separate the different kinds of factors:

$\dfrac{\left(6.673 \cdot 10^{-11}\frac{Nm^2}{kg^2} \right) \cdot (5.98 \cdot 1024\ kg) \cdot (70\ kg)}{(6.38 \cdot 10^6\ m)^2} =$ $\dfrac{6.673 \cdot 5.98 \cdot 1024 \cdot 70}{6.38 ^2} \cdot \dfrac{10^{-11}}{10^{12}} \cdot \dfrac{N \cdot m^2 \cdot kg \cdot kg}{kg^2 \cdot m^2}$