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In Mathematics / College | 2025-07-04

What is the product $(4.42 \times 10^3)(5 \times 10^4)$ written in scientific notation?
A. $9.42 \times 10^7$
B. $22.1 \times 10^7$
C. $2.21 \times 10^9$
D. $2.21 \times 10^8$

Asked by jptyson80

Answer (1)

Multiply the coefficients: 4.42 × 5 = 22.1 .
Multiply the powers of 10: 1 0 3 × 1 0 4 = 1 0 7 .
Combine the results: 22.1 × 1 0 7 .
Adjust to scientific notation: 2.21 × 1 0 8 . The final answer is 2.21 × 1 0 8 ​ .

Explanation

Understanding the Problem We are asked to find the product of two numbers expressed in scientific notation and express the result in scientific notation. The two numbers are 4.42 × 1 0 3 and 5 × 1 0 4 .

Multiplying Coefficients First, we multiply the coefficients: 4.42 × 5 = 22.1 .

Multiplying Powers of 10 Next, we multiply the powers of 10: 1 0 3 × 1 0 4 = 1 0 3 + 4 = 1 0 7 .

Combining Results Now, we combine the results: ( 4.42 × 5 ) × ( 1 0 3 × 1 0 4 ) = 22.1 × 1 0 7 .

Adjusting to Scientific Notation To express this in scientific notation, the coefficient must be between 1 and 10. Since 22.1 is not between 1 and 10, we need to adjust it. We can rewrite 22.1 as 2.21 × 1 0 1 . Therefore, 22.1 × 1 0 7 = ( 2.21 × 1 0 1 ) × 1 0 7 = 2.21 × ( 1 0 1 × 1 0 7 ) = 2.21 × 1 0 1 + 7 = 2.21 × 1 0 8 .

Final Answer Therefore, the product ( 4.42 × 1 0 3 ) ( 5 × 1 0 4 ) written in scientific notation is 2.21 × 1 0 8 .


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 the nearest star, Proxima Centauri, is approximately 4.017 × 1 0 13 kilometers. Similarly, the mass of an electron is about 9.109 × 1 0 − 31 kilograms. Multiplying these numbers might involve calculating the momentum of an electron traveling from a distant star, showcasing the practical application of scientific notation in complex calculations.

Answered by GinnyAnswer | 2025-07-04

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