Convert the following number into correct scientific notation.
[tex]
78.3 \times 10^{11}
{[] \times 10^{[]}}
[/tex]
Enter the coefficient in the green box and the exponent in the yellow box.
Answer (2)
Convert 78.3 to scientific notation: 78.3 = 7.83 × 1 0 1 .
Substitute back into the original expression: 78.3 × 1 0 11 = ( 7.83 × 1 0 1 ) × 1 0 11 .
Apply the exponent property: ( 7.83 × 1 0 1 ) × 1 0 11 = 7.83 × 1 0 12 .
The final answer in scientific notation is 7.83 × 1 0 12 .
Explanation
Understanding Scientific Notation Let's convert the given number, 78.3 × 1 0 11 , into correct scientific notation. Scientific notation requires the number to be in the form a × 1 0 b , where 1 ≤ a < 10 and b is an integer.
Converting 78.3 to Scientific Notation First, we need to express 78.3 in scientific notation. We can write 78.3 as 7.83 × 1 0 1 . This is because we move the decimal point one place to the left.
Substituting Back into the Original Expression Now, substitute this back into the original expression: 78.3 × 1 0 11 = ( 7.83 × 1 0 1 ) × 1 0 11 .
Applying the Exponent Property Using the property of exponents, which states that a m × a n = a m + n , we can simplify the expression:
( 7.83 × 1 0 1 ) × 1 0 11 = 7.83 × ( 1 0 1 × 1 0 11 ) = 7.83 × 1 0 1 + 11 = 7.83 × 1 0 12 .
Final Answer Therefore, the number in correct scientific notation is 7.83 × 1 0 12 .
Examples
Scientific notation is extremely useful in various fields. For instance, in astronomy, we use scientific notation to represent the vast distances between celestial objects. The distance to the Andromeda galaxy is approximately 2.5 × 1 0 22 meters. In chemistry, we use it to express the incredibly small sizes of atoms. The radius of a hydrogen atom is about 5.3 × 1 0 − 11 meters. Using scientific notation makes these numbers easier to work with and understand.
The number 78.3 × 1 0 11 can be expressed in scientific notation as 7.83 × 1 0 12 . The coefficient is 7.83 and the exponent is 12 . Thus, you enter 7.83 in the green box and 12 in the yellow box.
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