What single decimal multiplier would you use to increase by 1% followed by a 9% increase?

Explanation:

Let's say we had the starting amount of $100

Increasing this by 1% means we first take 1% of 100 to get 0.01*100 = 1, then we add it onto the original 100 getting us 100+1 = 101.

A shortcut is to multiply by 1.01; since 100% + 1% = 1.00 + 0.01 = 1.01

So 1.01*100 = 101

The multiplier shortcut is very handy if you want to chain together multiple percentage increases. If we want to tack on a 9% increase, we just multiply by 1.09 to get 1.09*101 = 110.09

The slower way would be to apply 9% to 101 getting 9.09, then adding that to 101.

Now let's go back to the starting amount $100

Multiply by the first multiplier 1.01 to get 1.01*100 = 101

Multiply by the second multiplier 1.09 to get 1.09*1.01*100 = 1.1009*100 = 110.09

The key difference in this section is how I multiplied out 1.01 and 1.09 first to get the new value 1.1009, which is the final combined multiplier. This effectively means the new price is 10.09% higher (after combining the 1% increase and the 9% increase) compared to the original $100.

Long story short, multiply the values 1.01 and 1.09 to get 1.1009