To express the number 0.0007 in standard index form, we need to rewrite it in the format [tex]\(a \times 10^b\)[/tex], where [tex]\(1 \leq a < 10\)[/tex] and [tex]\(b\)[/tex] is an integer.
Here are the steps to convert 0.0007 into standard index form:
1. Identify the Decimal Number:
We start with the number 0.0007.
2. Convert the Number into a Suitable Fraction:
Rewrite 0.0007 in a way that separates the significant digits from the power of 10. Observe where the decimal point would be placed to turn it into a number between 1 and 10. Essentially, you move the decimal point to the right until the number is between 1 and 10.
[tex]\[
0.0007 = 7 \times 10^{-4}
\][/tex]
3. Determine the Multiplier and the Exponent:
When moving the decimal point 4 places to the right to get from 0.0007 to 7:
- [tex]\(7\)[/tex] is the significant figure, [tex]\(a\)[/tex].
- We must account for moving the decimal point 4 places to the right, which corresponds to multiplying by [tex]\(10^{-4}\)[/tex].
4. Combine the Parts into Standard Index Form:
Thus, 0.0007 in standard index form is:
[tex]\[
7 \times 10^{-4}
\][/tex]
Therefore, the number 0.0007 written in standard index form is [tex]\(7 \times 10^{-4}\)[/tex].
