quantity 7 times 10 cubed end quantity times quantity 5.4 times 10 to the fourth power end quantity all divided by quantity 9 times 10 squared
a) 4.2 x 1010
b) 3.4 x 1010
c) 4.2 x 105
d) 3.4 x 105
To solve this problem, we need to first simplify the expression:
(7 * 10^3) * (5.4 * 10^4) / (9 * 10^2)
Simplifying the numerator:
(7 * 10^3) * (5.4 * 10^4) = 37.8 * 10^7
Since 37.8 is not in scientific notation, we convert it to scientific notation by moving the decimal point to the right until there is one non-zero digit to the left of the decimal point:
37.8 * 10^7 = 3.78 * 10^8
Now the expression becomes:
(3.78 * 10^8) / (9 * 10^2)
To divide these terms, subtract the exponents:
10^8 / 10^2 = 10^(8-2) = 10^6
The final answer is:
3.78 * 10^6
Therefore, the answer is:
c) 4.2 x 10^105
To solve this expression, follow these steps:
Step 1: Calculate the quantity 7 times 10 cubed. This equals 7 x (10^3) = 7,000.
Step 2: Calculate the quantity 5.4 times 10 to the fourth power. This equals 5.4 x (10^4) = 54,000.
Step 3: Multiply the result from step 1 (7,000) with the result from step 2 (54,000). This gives us 7,000 x 54,000 = 378,000,000.
Step 4: Calculate the quantity 9 times 10 squared. This equals 9 x (10^2) = 900.
Step 5: Divide the result from step 3 (378,000,000) by the result from step 4 (900). This gives us 378,000,000 / 900 = 420,000.
Therefore, the final answer is 4.2 x 10^5.
Therefore, the correct option is c) 4.2 x 10^5.
To evaluate the given expression, let's break it down step by step:
Step 1: Evaluate the quantity 7 times 10 cubed.
To do this, multiply 7 by 10 raised to the power of 3.
7 x 10^3 = 7,000
Step 2: Evaluate the quantity 5.4 times 10 to the fourth power.
Multiply 5.4 by 10 raised to the power of 4.
5.4 x 10^4 = 54,000
Step 3: Divide the result of Step 1 by the quantity 9 times 10 squared.
Divide the previous result (7,000) by 9 multiplied by 10 raised to the power of 2.
(7,000) / (9 x 10^2) = 7,000 / 900 = 7.7778
Step 4: Multiply the result of Step 3 by the result of Step 2.
Multiply 7.7778 by 54,000.
7.7778 x 54,000 = 419,999.2
Now, let's express the result in scientific notation:
419,999.2 can be written as 4.199992 x 10^5.
Therefore, the correct answer is:
c) 4.2 x 10^5