Allison's initial measurement of the side of the frame is 1.89 meters. We need to find a measurement for the opposite side that has the same digit in the ones place and satisfies the following conditions:
- The digit in the ones place must be the same as 1.89, which is 1.
- The digit in the tenths place must be 10 times the value of the digit in the hundredths place of the initial measurement (which is 9, since in 1.89 the hundredths digit is 9).
From the second condition, we have:
- The hundredths place of the original measurement (1.89) is 9.
- 10 times 9 is 90.
Since digits must be between 0 and 9, the tenths digit cannot be 90.
This implies the need to explore if there is a different interpretation of the instructions. Let's instead examine digits that could equal the next possible values leading towards a tenths digit that maintains logical coherence. The only possibility with a realistic approach:
- The hundredths can have values of 0, 1, ..., 8.
- Reassessing the tenths digit fulfilling that constraint - any digit multiplied by ten still adheres to a one-digit maximum, hence the only numerical candidate depends on values that fit in the scheme under ten per tenths - valid only if less than ten.
Thus, from candidates:
- 1.88 -> [tenths as 8, hundredths as 8 thus invalid]
- 1.79 -> [tenths as 7, hundredths is again disjointed]
- 1.8 -> [tenths as 8 computed under maximum digits fail]
- 1.9 -> [tenths as 9, hundredths 0 valid if treated through result]
Thus, out of the options provided, 1.90 meters, as the measurement up to the singular point showcases repurposing to reflect upon.
Hence, looking through these values for further concision lands upon D. 1.9 meters that layers appropriately under set conditions of digits presented.