What is the standard form of $3.43 \times 10^5$?
Answer (2)
We are given the number 3.43 × 1 0 5 in scientific notation.
We need to convert it to standard form by multiplying 3.43 by 1 0 5 = 100000 .
Multiplying 3.43 by 100000 is the same as moving the decimal point five places to the right.
Therefore, the standard form of 3.43 × 1 0 5 is 343000 .
Explanation
Understanding the Problem We are given the number 3.43 × 1 0 5 in scientific notation and asked to convert it to standard form. Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in standard form. A number in scientific notation is written as a × 1 0 b , where 1 ≤ ∣ a ∣ < 10 and b is an integer. To convert from scientific notation to standard form, we simply perform the multiplication.
Performing the Multiplication To convert 3.43 × 1 0 5 to standard form, we need to multiply 3.43 by 1 0 5 . Since 1 0 5 = 100000 , we have
3.43 × 1 0 5 = 3.43 × 100000
Multiplying 3.43 by 100000 is equivalent to moving the decimal point in 3.43 five places to the right. Thus,
3.43 × 100000 = 343000
Final Answer Therefore, the standard form of 3.43 × 1 0 5 is 343000 .
Examples
Scientific notation and standard form are useful in many real-world situations. For example, scientists use scientific notation to express very large or very small numbers, such as the distance to stars or the size of atoms. Engineers use scientific notation to express the values of components in electronic circuits. In everyday life, we might use scientific notation to express large amounts of money or population sizes. Understanding how to convert between scientific notation and standard form helps us to work with these numbers more easily. For instance, the distance to the Andromeda galaxy is approximately 2.5 × 1 0 22 meters. Writing this in standard form would be 25,000,000,000,000,000,000,000 meters, which is much less convenient.
To convert 3.43 × 1 0 5 to standard form, you multiply 3.43 by 1 0 5 , which equals 100000 . This results in moving the decimal point five places to the right, giving you 343000 . Hence, the standard form is 343000 .
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