Answer: the scale factor is 5^3 = 125; 3/8 = 0.375 Jose and Mei are talking about different kinds of decimal fractions, so it is hard to say whether they agree.Step-by-step explanation:1. 10 = 2·5, so a power of 10 is that power of 2 multiplied by that power of 5. 1000 = 10^3 = (2·5)^3 = (2^3)·(5^3) = 8·125To rewrite 3/8 as x/1000, both numerator and denominator must be multiplied by a scale factor of 125: 3/8 = (3·125)/(8·125) = 375/1000 = 0.375___2. Mei is correct that 2/3 can be written as (66 2/3)/100, which translates to the repeating decimal fraction ...[tex]\dfrac{2}{3}=0.66\overline{6}[/tex]Mei has essentially said she wants to write her fraction as the "terminating" decimal ...[tex]\dfrac{2}{3}=0.66\frac{2}{3}[/tex]That is not usually a recognized form for writing decimal fractions.If the numerator of the fraction with 100 as the denominator were a terminating decimal number, then the entire fraction would be a terminating decimal, in agreement with Jose's observation. For Mei's fraction, that is not the case, so Jose's observation does not apply.(The fraction 2/3 has a denominator of 3, which is not a power of 2 or 5 or 10, so cannot be scaled to be a power of 10.)