One of my lecturers today said that multiplying a number leaves the number of significant figures to which that number is correct unchanged, however it doesn't leave the number of decimal places correct.
He gave the following example: $128\times 0.99687$.
According to him, if 0.99687 is correct to 4 dp then the product is not correct to 4dp. However if 0.99687 is correct to 4sf then the product is also correct to 4sf.
I am struggling to see why this is the case. I have tried thinking about how decimal places differ from significant figures but I never really learned this in detail, only the "mechanics" of how to work dp's and sf's out, so any help would be appreciated.