Convert the following number into correct scientific notation.
[tex]
\begin{array}{l}
56.42 \times 10^{-6} \
{[?] \times 10^{[?]}}
\end{array}
[/tex]
Enter the coefficient in the green box and the exponent in the yellow box.
Coefficient
Answer (2)
The proper scientific notation for 56.42 × 1 0 − 6 is 5.642 × 1 0 − 5 , with a coefficient of 5.642 and an exponent of − 5 .
;
Move the decimal point in 56.42 one place to the left to obtain 5.642, which is between 1 and 10.
Increase the exponent of 10 by 1, so 1 0 − 6 becomes 1 0 − 5 .
Therefore, 56.42 × 1 0 − 6 = 5.642 × 1 0 − 5 .
The final answer is 5.642 × 1 0 − 5 .
Explanation
Understanding Scientific Notation We are given the number 56.42 × 1 0 − 6 and we want to convert it 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.
Adjusting the Coefficient The given number is 56.42 × 1 0 − 6 . The coefficient 56.42 is not between 1 and 10, so we need to adjust it. To do this, we move the decimal point one place to the left, which gives us 5.642.
Adjusting the Exponent Since we moved the decimal point one place to the left, we must increase the exponent of 10 by 1. So, 1 0 − 6 becomes 1 0 − 6 + 1 = 1 0 − 5 .
Final Scientific Notation Therefore, 56.42 × 1 0 − 6 = 5.642 × 1 0 − 5 . The coefficient is 5.642 and the exponent is -5.
Examples
Scientific notation is used in many fields, such as physics, astronomy, and chemistry, to represent very large or very small numbers. For example, the speed of light is approximately 3 × 1 0 8 meters per second, and the mass of an electron is approximately 9.11 × 1 0 − 31 kilograms. Using scientific notation makes it easier to work with these numbers and compare their magnitudes. Imagine calculating the distance light travels in a year - using scientific notation simplifies this calculation significantly!
