Calculate the following and state your answer in scientific notation:
\[\frac{(3 \times 10^2 \text{ kg})(4.0 \text{ km})}{5 \times 10^2 \text{ s}^2}\]
Answer (2)
The calculated value of 5 × 1 0 2 s 2 ( 3 × 1 0 2 kg ) ( 4.0 km ) is 2.4 × 1 0 3 kg m/s 2 . This result is expressed in scientific notation. Each step in the calculation maintains SI unit consistency and adheres to scientific notation rules.
;
To solve the given problem and express the answer in scientific notation, follow these steps:
Given: 5 × 1 0 2 s 2 ( 3 × 1 0 2 kg ) ( 4.0 km )
Step-by-step solution:
Convert units if necessary:
Here, 'km' is kilometers, which needs to be converted to meters (the standard unit) since kilograms and seconds are already in standard units.
1 kilometer = 1000 meters.
Therefore, 4.0 km = 4.0 × 1 0 3 m .
Substitute the converted value into the expression:
5 × 1 0 2 s 2 ( 3 × 1 0 2 kg ) ( 4.0 × 1 0 3 m )
Multiply the values in the numerator:
( 3 × 1 0 2 ) × ( 4.0 × 1 0 3 ) = 12.0 × 1 0 2 + 3 = 12.0 × 1 0 5
Now divide by the denominator:
Divide by 5 × 1 0 2 :
5 × 1 0 2 12.0 × 1 0 5 = 5 12.0 × 1 0 5 − 2
Calculate 5 12.0 = 2.4
So, the result is 2.4 × 1 0 3
Therefore, the result in scientific notation is: ( 2.4 \times 10^3 )
In this question, we performed unit conversions and applied the rules of scientific notation to solve a problem involving quantities in physics. This type of calculation helps to determine quantities like force, momentum, and various other physical properties when expressed in standard or scientific units.
