To convert the number [tex]\(123 \times 10^{-8}\)[/tex] into proper scientific notation, we'll follow these steps:
1. Understand the format of scientific notation: Scientific notation is written as [tex]\( a \times 10^b \)[/tex], where [tex]\(1 \leq a < 10\)[/tex] and [tex]\(b\)[/tex] is an integer.
2. Identify the coefficient and exponent:
- The given number is [tex]\(123 \times 10^{-8}\)[/tex].
- To adjust it into proper scientific notation, we need to move the decimal point in the number [tex]\(123\)[/tex] to the left so that we have a number between 1 and 10. Specifically, we shift the decimal point two places to the left to get 1.23.
3. Adjust the exponent accordingly:
- Moving the decimal point two places to the left decreases the power of 10 by 2.
- Since we initially had the exponent [tex]\(-8\)[/tex], we adjust it by adding 2 to it (because moving left is equivalent to adding to the exponent): [tex]\(-8 + 2 = -6\)[/tex].
Therefore, the number [tex]\( 123 \times 10^{-8} \)[/tex] in proper scientific notation is [tex]\( 1.23 \times 10^{-6} \)[/tex].
So, the coefficient is [tex]\( 1.23 \)[/tex] and the exponent is [tex]\(-6\)[/tex].
You should enter:
- 1.23 in the green box (representing the coefficient)
- -6 in the yellow box (representing the exponent)
