To express the number 0.0000407 in standard form, we need to follow a process that involves identifying a coefficient 'a' and an exponent 'b' such that the number can be written in the format [tex]\( a \times 10^b \)[/tex].
Here are the steps to convert 0.0000407 into standard form:
1. Identify the Decimal Point Adjustment:
First, recognize where the decimal place starts. In the number 0.0000407, the non-zero digits start at position 5 after the decimal point.
2. Move the Decimal Point:
Move the decimal point to the right until you have a number between 1 and 10. In this case, if you move the decimal to the right by 5 places, you get:
[tex]\[ 4.07 \][/tex]
3. Count the Number of Moves:
The number of positions you moved the decimal point determines the exponent of 10. Since we moved 5 places to the right, the exponent will be negative. Hence, we have:
[tex]\[ a = 4.07 \text{ and } b = -5 \][/tex]
4. Write in Standard Form:
Combine the coefficient and the exponent to express the number in standard form:
[tex]\[ 0.0000407 = 4.07 \times 10^{-5} \][/tex]
Thus, the standard form of 0.0000407 is:
[tex]\[ 4.07 \times 10^{-5} \][/tex]
