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The phrase "by approximately two fold" is correct and usable in written English.
You can use it when you want to describe an increase of a measurable quantity by a factor of two, such as in the following example sentence: "The popularity of the product increased by approximately two fold after its last marketing campaign."
Exact(4)
In our dataset, transcription of OX40 in the brain was increased by approximately two fold in moribund mice compared to non-moribund and resistant mice [11].
Ucp1 protein was also induced in the presence of T3 in differentiated wild type MEFs but its levels were increased by approximately two fold in differentiated Fsp27−/− MEFs (P<0.05).
Native GLP-1 increased cytokine production by approximately two fold in resting iNKT cells (IFN-γ p < 0.0001, IL-4 p < 0.005; Fig. 3a, b).
The D0 labelled peptide from the G9a/Glp1 knockdown sample was decreased by approximately two fold compared with the control, and MS/MS analysis of this D0 peak confirmed that this peptide contained the sequence pr-AAKprmeSAAKpr (pr = propionyl amide, +56 Da).
Similar(56)
For the week affected by the strike, traffic through the site increased by approximately five fold, generating 176,116 miles of walking routes and 'helping people burn off a possible 6.6 million calories'.
MiR-24 overexpression down regulated DHFR levels by approximately six fold as compared to Oligofectamine alone transfected cells (Fig. 4A), and conferred a morphological change resembling a differentiation-like phenotype in a colorectal cancer cell line (HCT-116-wt-p53).
Another nine genes, KCNQ1, KCNQ1OT1, NAP1L5, IPW, GNAS EXON 1A, SLC22A18, CDKN1C, MEST ISOFORM 2 and PEG10 were expressed at a level decreased by approximately ten fold relative to the three highly expressed genes, and the remaining 24 genes decreased by at least 100 fold.
Interestingly, in a xenograft model, CL4 fibro-blasts enhance the growth of mammary tumors by approximately eight- fold compared to CL3 cells, without a detectable increase in angiogenesis.
The expression of p22phox was significantly increased by approximately five fold in CsA-only treated rats (P < 0.05), and BIL pretreatment improved the expression of p22phox (P < 0.05).
HFE protein forms a stable complex with transferrin receptor (TFR), thereby reducing its affinity for transferrin (TF) by approximately ten fold [ 3].
ARE reporter gene activity was decreased by approximately four fold after introduction of Nrf2 KD or Jdp2 KD in WT MEFs in the absence and presence of TPA (Supplementary Figure S3), respectively.
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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