Example 3. Compare 76.7 and 400.05. Which is greater?

Since these numbers have digits to the left of the decimal place (they are greater than 1), we can just compare these digits. 400 is greater than 76, so 400.05 is greater than 76.7. In other words, 400.05 has a "4" in the hundreds place, and 76.7 has a "0" in the hundreds place (since it has no numeral in the hundreds place), making 400.05 greater than 76.7.

Example 4. Compare 45.91 and 45.618. Which is greater?

45.91 and 45.618 have the same numerals to the left of their decimal places (a "4" in the tens place and a "5" in the ones place). Therefore, we must look at their decimals, starting with the tenths place. Since 9 is greater than 6, 45.91 is greater than 45.618.