Sure! Let's convert the number [tex]\( 56.42 \times 10^{-6} \)[/tex] into correct scientific notation, step-by-step:
1. Identify the base number and the power of ten:
We start with [tex]\( 56.42 \times 10^{-6} \)[/tex]. The base number is [tex]\( 56.42 \)[/tex].
2. Normalize the base number:
In scientific notation, the base number (coefficient) must be between 1 and 10. To achieve this, we need to move the decimal point in [tex]\( 56.42 \)[/tex] so that it becomes a number between 1 and 10.
- Moving the decimal point one place to the left, [tex]\( 56.42 \)[/tex] becomes [tex]\( 5.642 \)[/tex].
3. Adjust the exponent accordingly:
When we move the decimal point one place to the left, we must increase the exponent by 1 to balance the equation. Initially, the exponent is [tex]\( -6 \)[/tex]. By moving the decimal point one place to the left, the new exponent becomes:
- [tex]\( -6 + 1 = -5 \)[/tex].
So, the given number [tex]\( 56.42 \times 10^{-6} \)[/tex] in scientific notation is [tex]\( 5.642 \times 10^{-5} \)[/tex].
Therefore:
- The coefficient is [tex]\( 5.642 \)[/tex].
- The exponent is [tex]\( -5 \)[/tex].
