Sure, let's write the numerical value 0.00000025 in scientific notation step-by-step.
### Step-by-Step Solution:
1. Understand what scientific notation is:
- Scientific notation is a way of expressing a number as the product of a number (a) and a power of 10 (10^b).
- The format is [tex]\( a \times 10^b \)[/tex], where:
- [tex]\( a \)[/tex] is a number greater than or equal to 1 and less than 10.
- [tex]\( b \)[/tex] is an integer.
2. Identify the given number:
- The given number is 0.00000025.
3. Determine the number [tex]\( a \)[/tex]:
- Move the decimal point in the number 0.00000025 to the right until you have a number between 1 and 10.
- In this case, moving the decimal 7 places to the right gives us 2.5.
- Therefore, [tex]\( a = 2.5 \)[/tex].
4. Determine the exponent [tex]\( b \)[/tex]:
- Since we moved the decimal point 7 places to the right, we need to express this shift using a power of 10.
- Moving the decimal point to the right corresponds to a negative exponent.
- Therefore, [tex]\( b = -7 \)[/tex].
5. Write the number in scientific notation:
- Combine [tex]\( a \)[/tex] and [tex]\( b \)[/tex] to get the scientific notation format.
- The scientific notation of the given number 0.00000025 is [tex]\( 2.5 \times 10^{-7} \)[/tex].
### Final Answer:
[tex]\[ 0.00000025 \text{ in scientific notation is } 2.5 \times 10^{-7} \][/tex]
That's how you can convert the numerical value 0.00000025 into scientific notation.
