In the following, round to the indicated place value.

$$\begin{gathered} \left(a\right)28,166 \\ \left(b\right)481,628 \end{gathered}$$

• Look at the number that has to be rounded.
• We note the digit at the hundredths place because we need to round the given decimal number to the nearest hundredth.
• Next, look to the right of the hundredths column for the 'thousandths' place digit.
• If the thousandths place digit is less than $5,$we keep the hundredths place digit and delete all the digits to its right.
• If the digit in the thousandths place is $5$or greater, we add $1$to the digit in the hundredths place, increasing the hundredths place by $1$and removing all digits to its right.

(a) The given number is:

$28,166$

• It is known that if the number you are rounding is followed by $5,6,7,8or9,$the number is followed should be rounded up.
• The hundreds digit in the number is $1.$

Since the hundred digit $1$is followed by the tens digit $6,$therefore round up the digit $1$to $2$and add zeroes:

$28200$

(b) $481,628$

• The hundreds digit in the number is $6.$

Since the hundred digit $6$is followed by the tens digit $2,$which is near to $0$therefore the digit $6$to will not change and add zeroes in place of $28:$

$481600$

(a) The rounded value of the number to the nearest hundred is$28200.$

(b) The rounded value of the number to the nearest hundred is$481600.$