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The phrase "to their understanding" is correct and usable in written English
It can be used when referring to someone's comprehension or interpretation of a subject or situation. Example: "The teacher explained the concept in simple terms to their understanding."
Exact(59)
As indicated in previous research, parents generally understand research, but appreciate that there are limits to their understanding about the nuances of research aims, methods and implications (Klima et al. 2014).
Will this make a difference to their understanding of these artists?
"Gay marriage is contrary to their understanding of Scripture," Mr. Coates said.
How does it add to their understanding of the idea of citizenship?
People are invited to see both plays at separate performances but that is not essential to their understanding either one.
Improvements in instrumentation, however notably DC amplifiers and spacecraft-borne devices—have contributed significantly to their understanding.
According to their understanding, the Obama administration sees the Copenhagen accord and the promise of $30bn in climate aid for poor countries as combined package.
Amid the relatively placid economic period of the Great Moderation, economists did little to add to their understanding of large, global crises.
Judges were left to decide cases according to their understanding of Shariah codes, which were seen as permitting the mild application of violence against "disobedient" wives.
Our Big Tenant Survey has gathered responses from more than 61,000 social housing tenants on a range of issues from how they feel about their landlord to their understanding of welfare reforms.
TOWARD that end, the medical students hold a convocation of thanks each spring at the completion of their anatomy course work to acknowledge the gift of the human body that has contributed to their understanding of medicine.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com