Determine the sum. Write your answer in scientific notation. [tex]4.4 \times 10^4+12.3 \times 10^4=[/tex]
Answer (2)
Factor out the common term: ( 4.4 + 12.3 ) × 1 0 4 .
Add the numbers: 4.4 + 12.3 = 16.7 .
Rewrite in scientific notation: 16.7 × 1 0 4 = 1.67 × 1 0 1 × 1 0 4 = 1.67 × 1 0 5 .
The final answer is 1.67 × 1 0 5 .
Explanation
Understanding the problem We are asked to determine the sum of 4.4 × 1 0 4 and 12.3 × 1 0 4 and express the result in scientific notation.
Factoring out the common term To add these two numbers, we can factor out the common term 1 0 4 :
4.4 × 1 0 4 + 12.3 × 1 0 4 = ( 4.4 + 12.3 ) × 1 0 4
Adding the numbers Now, we add the numbers inside the parentheses: 4.4 + 12.3 = 16.7 So, we have 16.7 × 1 0 4 .
Expressing in scientific notation To express this in scientific notation, we need to write the number in the form a × 1 0 b , where 1 ≤ a < 10 and b is an integer. In our case, we have 16.7 × 1 0 4 . We can rewrite 16.7 as 1.67 × 1 0 1 . Therefore, 16.7 × 1 0 4 = ( 1.67 × 1 0 1 ) × 1 0 4 = 1.67 × ( 1 0 1 × 1 0 4 ) = 1.67 × 1 0 1 + 4 = 1.67 × 1 0 5
Final Answer The sum in scientific notation is 1.67 × 1 0 5 .
Examples
Scientific notation is used in many fields, such as physics, astronomy, and engineering, to represent very large or very small numbers. For example, the distance to the nearest star, Proxima Centauri, is approximately 4.017 × 1 0 16 meters. Similarly, the size of an atom is approximately 1 × 1 0 − 10 meters. Using scientific notation makes it easier to work with these numbers and compare their magnitudes.
The sum of 4.4 × 1 0 4 and 12.3 × 1 0 4 is 1.67 × 1 0 5 when written in scientific notation. We factored out the common term, added the coefficients, and converted the result to the proper form. This process ensures we express numbers correctly in scientific notation.
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