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The First Minister also said Royal Bank of Scotland's statement that it would move its headquarters out of an independent Scotland did not mean jobs would go.
Campaigning at Bruntsfield in Edinburgh Southern, she said: "RBS said the same thing in 2014. They were at pains to stress then and they're at pains to stress now that they're talking about their registered office, not their operations, not jobs.
"I'm never complacent about business location and jobs and it's incumbent on me and the SNP and anyone in government to engage constructively with businesses of all sizes, but it is also important we don't misrepresent what RBS is actually saying - and I think after the experience of 2014 that's something people get."
The latest poll by Savanta ComRes for The Scotsman earlier this week, showed 46 per cent for independence and 54 per cent against, once don't knows are excluded – almost back down to the figures in the 2014 referendum.
But Ms Sturgeon said: "Polls generally on independence show it's at a much higher level of support than it was in 2014 and that's good.
"Polls will fluctuate, but if there is a lesson for Yes supporters and the independence movement it's that we can't take support for granted, we can't assume that we've done all the work and it's just a case now of engineering our way to independence.
"There are voices in this campaign in the independence movement that are talking more about how you game your way to independence as opposed to how you persuade your way to independence.
"I wouldn't read too much into one poll but if I was to read anything into it it would be that it is a reminder to those of us who want to achieve independence that you have to do that properly through persuasion and building a case."
The poll also suggested the SNP would fail to get an overall majority of seats at Holyrood and would have to rely on the Greens for a pro-independence majority.
Ms Sturgeon said she had never assumed the SNP would get an overall majority.
"The Holyrood election system is designed to prevent a party getting an overall majority. I personally have never set that as the benchmark of the SNP's campaign. "We're campaigning to win. If we can poll high enough and win a majority that would be fantastic but the important thing is to win the election so we can get back to work steering the country through the pandemic and into recovery.
"People think the outcome of the election is a foregone conclusion but very tight margins are always at play in Holyrood elections so if people want a re-elected SNP government, if they want me back at work the week after the election steering the country through, they’ve got to come out and vote for it.”
During her campaign stop Ms Sturgeon dropped in at the Maytree coffee shop in Bruntsfield Place and several other local shops with Edinburgh Southern SNP candidate Catriona MacDonald.