Your English writing platform
Discover LudwigExact(2)
British mathematician William Shanks famously took 15 years to calculate to 707 digits, but made a mistake in the 528th digit, rendering all subsequent digits incorrect.
However, the distribution flattens out progressively for subsequent digits and the difference is only 12.0% for 0 and 8.5% for 9 for the second digit (and 10.2% and 9.8% respectively for the third digit).
Similar(54)
Commenting on these algorithms, Liu Hui suggested that one could continue computing the nonintegral portion of a root in the same way, setting 10 as denominator for the first subsequent digit, 100 as denominator for the first two digits, and so on; he thus gave the root in terms comparable to decimal fractions.
Once the correct stratum is established at baseline, the patient is given the subsequent unique four-digit randomisation number from his/her stratum on the randomisation list.
Grafts were placed at different antero-posterior levels in wing buds, using somites and somite boundaries as reference points [33 (Figure 5A,C insets)] and the subsequent contribution to the digits was assessed in 10 day wings ( Figure 5C).
During the fall, they attempted to read the digits for subsequent report.
Results: When the transpalmar response was absent, subsequent median-ulnar to digit 4 testing and median-radial to digit 1 testing yielded responses in 6% and 8% of cases, respectively.
In such postal documents, determination of the script of the handwritten postal codes is crucial for subsequent invocation of the digit recognizers for respective scripts.
The present longitudinal study investigated whether children's numerical processing skills at the start of formal schooling predict subsequent development in single-digit arithmetic and fact retrieval.
When the median-ulnar to digit 4 response was absent, subsequent transpalmar and median-radial to digit 1 testing yielded responses in 39% and 32% of cases, respectively.
But Martin's carries were in double digits in every subsequent game as the Jets went on to win the American Football Conference East title.
Write better and faster with AI suggestions while staying true to your unique style.
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