To convert the given number [tex]\( 0.065 \times 10^8 \)[/tex] into scientific notation, follow these steps:
1. Identify the Goal: Scientific notation expresses numbers as [tex]\( a \times 10^n \)[/tex], where [tex]\( a \)[/tex] is a number greater than or equal to 1 and less than 10, and [tex]\( n \)[/tex] is an integer.
2. Adjust the Coefficient: Start with the given number [tex]\( 0.065 \)[/tex]. This number is not within the range of 1 to 10 yet, so we need to adjust it. Multiply the coefficient [tex]\( 0.065 \)[/tex] by 10 to move the decimal place one position to the right. This operation changes [tex]\( 0.065 \)[/tex] to [tex]\( 0.65 \)[/tex].
3. Adjust the Exponent: Each time you multiply the coefficient by 10, you have to adjust the exponent accordingly. Since we multiplied [tex]\( 0.065 \)[/tex] by 10 (which is equivalent to [tex]\( 10^1 \)[/tex]), we must decrease the exponent of [tex]\( 10 \)[/tex] in [tex]\( 10^8 \)[/tex] by 1. So, the new exponent becomes [tex]\( 7 \)[/tex] ( [tex]\( 8 - 1 = 7 \)[/tex] ).
4. Write the Result: Combine the adjusted coefficient and the adjusted exponent to form the correct scientific notation.
Hence,
[tex]\[ 0.065 \times 10^8 \][/tex]
can be written in scientific notation as:
[tex]\[ 0.65 \times 10^7 \][/tex]
Coefficient (Green Box): 0.65
Exponent (Yellow Box): 7
