To determine the value of [tex]\( n \)[/tex] when the number 0.000053 is written in scientific notation, follow these steps:
1. Understand Scientific Notation: Scientific notation expresses numbers as a product of a coefficient (a number between 1 and 10) and a power of 10. The general form is [tex]\( a \times 10^n \)[/tex], where [tex]\( 1 \leq a < 10 \)[/tex].
2. Identify the Coefficient: The number 0.000053 can be converted to scientific notation by adjusting the decimal point. Move the decimal point to the right until you get a number between 1 and 10.
0.000053 can be rewritten as 5.3.
3. Count the Number of Decimal Places Moved: To convert 0.000053 to 5.3, the decimal point needs to be moved 5 places to the right.
4. Determine the Exponent [tex]\( n \)[/tex]: Since we moved the decimal point to the right, the exponent [tex]\( n \)[/tex] will be negative. Each move of the decimal to the right corresponds to multiplying by [tex]\( 10^{-1} \)[/tex]. Thus, moving 5 places to the right, you get an exponent of -5.
Therefore, 0.000053 in scientific notation is [tex]\( 5.3 \times 10^{-5} \)[/tex].
Hence, the value of [tex]\( n \)[/tex] is [tex]\(-5\)[/tex].
