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The phrase "approximately the same numbers" is correct and usable in written English.
It can be used when discussing quantities or values that are close to each other but not exactly the same.
Example: "The two groups had approximately the same numbers of participants, making the comparison valid."
Alternatives: "roughly equivalent figures" or "about the same quantities".
Exact(8)
The ratio is close to one for all samples indicating that approximately the same numbers of segments are detected irrespective of fraction of normal cells that varied between 1% and 26%.
LVSΔ1423/1422 from the high dose challenge was recovered from lungs (Fig. 10A) and liver (Fig. 10B) in approximately the same numbers as LVS on day-2 and day-4 PI, but was recovered in significantly fewer numbers from lungs, liver, and spleen on day-7 PI (P<0.005 for each organ).
For the purpose of our investigation, we decided to include approximately the same numbers of adolescents with asthma and epilepsy.
The sample was stratified to recruit approximately the same numbers of people in each of the three age strata: 65 74, 75 84, 85+ [ 9].
For at least four of the cases, there were approximately the same numbers of positive and negative evaluations of the same cholesterol value.
We were able to extract approximately the same numbers of orthologous tRNAs for all pairs (a list of genomic positions is available from the authors upon request).
Similar(52)
Approximately the same number are taking the lead in security operations or are "fully independent".
In approximately the same number of at-bats, he hit 16 the season before and 18 the season after.
But there have been approximately the same number of male and female judges (though no woman has yet chaired the judges).
While both counties serve approximately the same number of people, most of Nassau's strips have been absorbed into its established downtown business districts, Mr. Fedelem said.
Approximately the same number vote in school board elections in May, when the ballot includes the school budget and the library budget.
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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