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) = 8·125
To 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
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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.)
