The phrase “in a significant decline” is correct and usable in written English.
You can use it to describe a decrease in something such as a quantity or a value. For example: "The number of endangered species has been in a significant decline over the past decade."
The computer revolution has resulted in a significant decline in the number of handwritten manuscripts produced.
Social mobility in the accountancy profession has been in a significant decline, according to the Social Mobility and Child Poverty Commission.
A truce between the country's two main street gangs that was brokered by Roman Catholic clerics in 2012 resulted in a significant decline in the homicide rate.
In March 2012 mediation by Roman Catholic clerics led to a truce between the gangs that resulted in a significant decline in the country's skyrocketing homicide rate.
If thimerosal is an important cause, the phasing out of its use in vaccines that is now occurring should result in a significant decline in cases in the next few years.
Further pH increase or decrease beyond this resulted in a significant decline of activity and biomass yield for all isolates.
Although the UK isn't the most exposed of the G7's main economies to a slowdown in China, a significant decline in Chinese imports could lead to a substantial loss for the British economy.
In contrast, a significant decline in vaccine-specific CD8+ T cells was observed.
In addition, a significant decline of medium spiny neuron density was observed from days 7 to 16.
Also, Community Networks MI-MeSH (introduced in 1996) saw a significant decline in output in the 2002 2006 period.
None of that, or very little, has happened so far, not even in California, despite a significant decline in tax revenue.
