Certainly! Let's convert the number [tex]\( 68.46 \times 10^{-3} \)[/tex] into proper scientific notation.
### Step-by-Step Solution:
1. Identify the given number and its exponent:
The number given is [tex]\( 68.46 \)[/tex] and it is multiplied by [tex]\( 10^{-3} \)[/tex].
2. Normalizing the coefficient:
We need the coefficient to be a number between 1 and 10, so we must adjust the position of the decimal point in [tex]\( 68.46 \)[/tex]:
- To convert [tex]\( 68.46 \)[/tex] into a number between 1 and 10, we move the decimal point one place to the left.
- Moving the decimal point one place to the left gives us [tex]\( 6.846 \)[/tex].
3. Adjust the exponent:
Moving the decimal point one place to the left in the coefficient (from 68.46 to 6.846) effectively divides the number by 10. To balance this change, we need to increase the exponent by 1.
- The original exponent is [tex]\( -3 \)[/tex].
- Increasing the exponent [tex]\( -3 \)[/tex] by 1 (because we divided the coefficient by 10) results in an exponent of [tex]\( -2 \)[/tex].
4. Combine the new coefficient and exponent:
Therefore, the number [tex]\( 68.46 \times 10^{-3} \)[/tex] in correct scientific notation is written as:
[tex]\[
6.846 \times 10^{-2}
\][/tex]
### Final Answer:
- Coefficient: [tex]\( 6.846 \)[/tex] (enter this in the green box)
- Exponent: [tex]\( -2 \)[/tex] (enter this in the yellow box)
So, the number [tex]\( 68.46 \times 10^{-3} \)[/tex] in scientific notation is:
[tex]\[
6.846 \times 10^{-2}
\][/tex]
This concludes our conversion into scientific notation!
