What is $4.05 \times 10^6$ written in standard form?
A. 405,000
B. 4,050,000
C. 40,500,000
D. 40,500
Answer (2)
We are given the number 4.05 × 1 0 6 in scientific notation.
To convert to standard form, we multiply 4.05 by 1 0 6 which equals 1,000,000.
Performing the multiplication, we get 4.05 × 1 , 000 , 000 = 4 , 050 , 000 .
Thus, the standard form of 4.05 × 1 0 6 is 4 , 050 , 000 .
Explanation
Understanding the Problem We are given a number in scientific notation, which is 4.05 × 1 0 6 , and we need 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.
Converting to Standard Form To convert a number from scientific notation to standard form, we need to multiply the decimal number by the power of 10. In this case, we have 4.05 × 1 0 6 . This means we need to multiply 4.05 by 1 0 6 , which is 1,000,000.
Performing the Multiplication Multiplying 4.05 by 1,000,000 is the same as moving the decimal point 6 places to the right. So, we have:
4.05 × 1 , 000 , 000 = 4 , 050 , 000
Final Answer Therefore, 4.05 × 1 0 6 in standard form is 4,050,000.
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 between stars or the size of an atom. In finance, large amounts of money are often expressed in standard form, such as the national debt or the budget of a large corporation. Understanding how to convert between scientific notation and standard form is a valuable skill for anyone working with numbers in these fields. Imagine you are calculating the total revenue of a company that sells 4.05 million units of a product priced at $1 each. Expressing 4.05 million as 4.05 × 1 0 6 helps in understanding the magnitude, and converting it to standard form, 4,050,000, makes it easier to use in calculations and reports.
The number 4.05 × 1 0 6 is converted to standard form by multiplying 4.05 by 1 0 6 , which equals 1,000,000. The result is 4,050,000, making the correct answer B. 4,050,000 .
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