Determine the difference. Write your answer in scientific notation. [tex]$33.4 imes 10^7-12.3 imes 10^9=$[/tex] ?

Question

Determine the difference. Write your answer in scientific notation. [tex]$33.4 	imes 10^7-12.3 	imes 10^9=$[/tex] ?

GinnyAnswer · Answer

Convert both numbers to the same power of 10: 33.4 × 1 0 7 = 0.334 × 1 0 9 . 
 Subtract the numbers: ( 0.334 − 12.3 ) × 1 0 9 = − 11.966 × 1 0 9 . 
 Convert the result to scientific notation: − 11.966 × 1 0 9 = − 1.1966 × 1 0 10 . 
 The final answer is: − 1.1966 × 1 0 10 ​ . 
 
 Explanation 
 
 Understanding the Problem We are asked to find the difference between two numbers expressed in scientific notation: 33.4 × 1 0 7 and 12.3 × 1 0 9 . The answer should be written in scientific notation. 
 
 Equalizing Powers of 10 To subtract these numbers, we need to express them with the same power of 10. Let's convert both numbers to 1 0 9 . 
 
 Converting the First Term We can rewrite 33.4 × 1 0 7 as 0.334 × 1 0 9 . This is because 33.4 × 1 0 7 = 33.4 × 1 0 − 2 × 1 0 9 = 0.334 × 1 0 9 . 
 
 Subtracting the Numbers Now, we subtract the two numbers: ( 0.334 × 1 0 9 ) − ( 12.3 × 1 0 9 ) = ( 0.334 − 12.3 ) × 1 0 9 . 
 
 Calculating the Difference Calculating the difference 0.334 − 12.3 , we get − 11.966 . Therefore, the expression becomes − 11.966 × 1 0 9 . 
 
 Expressing in Scientific Notation To express the result in scientific notation, a × 1 0 b , where 1 ≤ ∣ a ∣ < 10 and b is an integer, we rewrite − 11.966 × 1 0 9 as − 1.1966 × 1 0 10 . 
 
 Final Answer Thus, the difference 33.4 × 1 0 7 − 12.3 × 1 0 9 = − 1.1966 × 1 0 10 .

Examples 
 Scientific notation is extremely useful in fields like astronomy and physics, where dealing with very large or very small numbers is common. For instance, the distance to a star might be 4.5 × 1 0 16 meters, and the size of an atom might be 1.2 × 1 0 − 10 meters. Performing calculations with these numbers is much easier when they are expressed in scientific notation. Understanding how to manipulate and subtract numbers in scientific notation is crucial for these types of calculations.

Anonymous · Answer

The difference between 33.4 × 1 0 7 and 12.3 × 1 0 9 is calculated by first converting them to the same power of 10, allowing for easy subtraction. The result is − 11.966 × 1 0 9 , which is expressed in scientific notation as − 1.1966 × 1 0 10 . 
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Determine the difference. Write your answer in scientific notation. [tex]$33.4 \times 10^7-12.3 \times 10^9=$[/tex] ?

Answer (2)

Determine the difference. Write your answer in scientific notation. [tex]$33.4 \times 10^7-12.3 \times 10^9=$[/tex] ?

Answer (2)

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