## Thinking Mathematically (6th Edition)

a. $19,465,200$ b. $19,465,000$ c. $19,470,000$ d. $19,500,000$ e. $19,000,000$ f. $20,000,000$
The provided population of the state of New York in the exercise is $19,465,197$. To do this exercise, we need to remember how we round numbers: 1. Look at the digit to the right of the digit where rounding is to occur. 2a. If the digit to the right is $5$ or greater, add $1$ to the digit to be rounded. 2b. If the digit to the right is less than $5$, do not change the digit to be rounded. 3. Replace all digits to the right with zeros. a.Rounding to nearest hundred: The hundreds digit is $1$, and the digit behind it is $9$, which is greater than $5$; therefore, we have to increase the hundreds digit by $1$, giving us the following number: $19,465,200$ b.Rounding to nearest thousand: The thousands digit is $5$, and the digit behind it is $1$, which is less than $5$; therefore, we have to keep the thousands digit the same, giving us the following number: $19,465,000$ c.Rounding to nearest ten thousand: The ten thousands digit is $6$, and the digit behind it is $5$, and therefore we have to increase the ten thousands digit by $1$, giving us the following number: $19,470,000$ d.Rounding to nearest hundred thousand: The hundred thousands digit is $4$, and the digit behind it is $6$, which is greater than $5$; therefore, we have to increase the hundred thousands digit by $1$, giving us the following number: $19,500,000$ e.Rounding to nearest million: The millions digit is $9$, and the digit behind it is $4$, which is less than $5$; therefore, we have to keep the millions digit the same, giving us the following number: $19,000,000$ f.Rounding to nearest ten million: The ten millions digit is $1$, and the digit behind it is $9$, and therefore we have to increase the ten millions digit by $1$, giving us the following number: $20,000,000$