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People often say that percentages greater than 100 make no sense because you can't have more than all of something. This is simply silly and mathematically ignorant. A percentage is just a ratio between two numbers.
Understanding the Context
There are many situations where it is perfectly reasonable for the numerator of a fraction to be greater than the denominator. The flow rate increases 100-fold (one hundred-fold) Would be a more idiomatic way of saying this, however, the questioner asks specifically about the original phrasing. The above Ngram search would suggest that a one hundred has always been less frequently used in written language and as such should probably be avoided. Your other suggestion of by one hundred times is definitely better than a ...
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relating to 100 years : marking or beginning a century, with the example "the centurial years 1600 and 1700". But there is a word that is widely used to indicate the range of years or centuries covered by an article or book: history. If soap A kills 100% and soap B kills 99.99% of bacteria, the remaining amount of bacteria after applying A (0%) is infinitely smaller than the remaining amount of bacteria after applying B (0.01%). Therefore A is much, much better. You can see from these examples that 0.01% gap behaves differently across the percentage scale.
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37 Wikipedia lists large scale numbers here. As only the 10 x with x being a multiple of 3 get their own names, you read 100,000,000,000,000,000,000 as 100 * 10 18, so this is 100 quintillion in American and British English and 100 trillion in most (non-English speaking) other places. The type of writing you are doing also plays into your decision. For example, in legally binding documents, like contracts or exhibits to contracts, the spelled out number is the legally binding number. So if a text said that, "you are 99% (one-hundred percent) responsible", the 100% number would be legally binding, not 99%. Is It Ok To Write "100%" In A Formal Text?
- English Language & Usage ... 2 Use 100% when you are stating mathematical thought like statistics. Use "one hundred percent" when you are stating non-mathematical thought like a story.