Express the number in standard notation.
$5 \times 10^7$
Answer (2)
Multiply 5 by 1 0 7 .
Recognize that 1 0 7 = 10 , 000 , 000 .
Calculate 5 × 10 , 000 , 000 = 50 , 000 , 000 .
Express the final answer in standard notation: 50 , 000 , 000 .
Explanation
Understanding the Problem We are given the number 5 × 1 0 7 in scientific notation and asked to express it in standard notation. Standard notation is the way we usually write numbers.
Converting to Standard Notation To convert from scientific notation to standard notation, we need to multiply the number 5 by 1 0 7 . The exponent 7 tells us how many places to move the decimal point in 5 to the right. Since 1 0 7 = 10 , 000 , 000 , we are multiplying 5 by 10,000,000.
Performing the Multiplication Multiplying 5 by 10,000,000, we get:
5 × 10 , 000 , 000 = 50 , 000 , 000
Final Answer Therefore, the number 5 × 1 0 7 in standard notation is 50,000,000.
Examples
Scientific notation is useful in many real-world situations, especially when dealing with very large or very small numbers. For example, the distance from the Earth to the Sun is approximately 1.5 × 1 0 11 meters. Writing this in standard notation would be 150,000,000,000 meters, which is more cumbersome. Similarly, in computer science, the size of a file might be expressed as 2.5 × 1 0 6 bytes, which is 2,500,000 bytes in standard notation. Using scientific notation makes these numbers easier to handle and understand.
The number 5 × 1 0 7 expressed in standard notation is 50,000,000. This involves multiplying 5 by 10 , 000 , 000 , which is 1 0 7 . Therefore, the final result is 50 , 000 , 000 .
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