#### Answer

a. $19,465,200$
b. $19,465,000$
c. $19,470,000$
d. $19,500,000$
e. $19,000,000$
f. $20,000,000$

#### Work Step by Step

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:
$20,000,000$