Women first began working outside the home during the industrial revolution, mostly in textile mills. The Merrimack Manufacturing Company opened more than thirty mills in 1840, employing more than 7,00 workers- mostly unmarried women. So, many women worked outside the home before the Civil war, though many point to the World War 2 era.
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When working with really large or really small numbers.
Scientific notation produces convenient numbers when working with very small or very large quantities.
Working with very large or very small numbers, in economics or science, for example.
There are many different standard forms: standard forms of numbers, of linear equations, of circles, etc. The standard form of numbers simplifies working with very large and very small numbers.
Hundred googolplexian and one! There is no end to the list of integers; we don't have names for very large numbers - practically, there are very approximately 1040 atoms in the universe - less than half a google - so there isn't much call for very large numbers outside of mathematics.