Question

what is $7,828.1895 rounded to the nearest cent?
$7,828.20
$7,828.18
$7,828.00
$7,828.19

Explanation:

Step1: Identify the digit to round

The number is \$7,828.1895. We need to round to the nearest cent, which is the hundredths place (the second decimal place). The digit in the hundredths place is 8, the digit in the thousandths place is 9, and the ten - thousandths place is 5.

Step2: Apply the rounding rule

When rounding, if the digit to the right of the place we are rounding to (the thousandths place here, digit 9) is 5 or greater, we round up the digit in the hundredths place. But wait, actually, let's look at the number more carefully. The number is 7828.1895. To round to the nearest cent (two decimal places), we look at the third decimal place (thousandths place) which is 9, and the fourth decimal place is 5. But when rounding to two decimal places, we consider the digit in the third decimal place. Since 9 is greater than or equal to 5, we round up the second decimal place. The second decimal place is 8, and the third is 9. Wait, no, let's do it step by step. The number is 7828.1895. The first decimal place is 1 (tenths), second is 8 (hundredths), third is 9 (thousandths), fourth is 5 (ten - thousandths). When rounding to the nearest cent (hundredths place), we look at the thousandths place digit (9). Since 9 ≥ 5, we add 1 to the hundredths place. But 8 + 1 = 9? Wait, no, wait the number is 7828.1895. Wait, maybe I made a mistake. Wait, 7828.1895: the hundredths digit is 8, the thousandths digit is 9. So when rounding to the nearest cent, we take the number up to the hundredths place, and look at the thousandths digit. Since 9 > 5, we round up the hundredths place. But 8 + 1 = 9? Wait, no, wait 7828.1895. Let's write it as 7828.18 (hundredths place) with the remaining digits 95. Wait, another way: 7828.1895. To round to two decimal places, we can use the formula for rounding: if the digit in the (n + 1)th decimal place ≥ 5, then the nth decimal place digit is increased by 1. Here, n = 2 (hundredths place), the (n+1)th digit (thousandths place) is 9 ≥ 5. So the hundredths place digit 8 becomes 8 + 1 = 9? But wait, the option has \$7,828.19. Wait, maybe I messed up the places. Wait, 7828.1895: the decimal part is 0.1895. The first decimal: 1 (tenths), second: 8 (hundredths), third: 9 (thousandths), fourth: 5 (ten - thousandths). When rounding to the nearest cent (two decimal places), we look at the third decimal (9). Since 9 ≥ 5, we round up the second decimal. But 8 + 1 = 9, so the number becomes 7828.19? Wait, no, wait 0.1895 rounded to two decimal places: 0.19, because 0.1895 is closer to 0.19 than to 0.18. So 7828.1895 rounded to the nearest cent is 7828.19.

Answer:

\$7,828.19