Problem 69 - Prealgebra

Question

Round 79.369 to the nearest hundredth.

Step-by-Step Solution

Answer

79.37

Step 1: Identify the Rounding Position

To round to the nearest hundredth, we need to look at the number in the hundredths place. In 79.369, the hundredths place is occupied by the digit 6.

Step 2: Locate the Decision Digit

To decide if we round the hundredths place up or leave it as is, we need to check the digit immediately to the right of the hundredths place. In 79.369, this is the digit 9 in the thousandths place.

Step 3: Apply Rounding Rules

According to rounding rules, if the decision digit (the digit in the thousandths place here) is 5 or more, we round up the digit in the hundredths place by one. Since 9 is greater than 5, we round the 6 up to 7.

Step 4: Write the Rounded Number

After rounding, we replace everything after the hundredths position with zeroes or simply disregard those digits. Therefore, 79.369 rounded to the nearest hundredth is 79.37.

Key Concepts

Place Value

Understanding place value is essential when working with numbers of any size. Each digit in a number has a specific value, depending on its position. Let's break down the placement to make it clear:

• Units: The place holding whole number values.
• Tens, Hundreds, Thousands: Each position to the left increases the value by a factor of ten.
• Tenths, Hundredths, Thousandths: Each position to the right of the decimal point decreases the value by one-tenth of the previous position.

So, in the number 79.369, understanding that the '6' is in the hundredths place means recognizing that its value is six hundredths, or 0.06. Paying attention to place value helps ensure accuracy when rounding numbers.

Hundredths Place

The hundredths place is the second position to the right of the decimal in a number. It is crucial for precise measurements or when dealing with money. For example, in 79.369, the hundredths digit is 6. This tells us the number has an additional 6 cents if you think of it in terms of currency. When you round a number to the nearest hundredth, this digit is central. By focusing on this digit, you can determine the number's approximate value based on specific criteria, which we discuss in the next section on rounding rules. Properly identifying the hundredths place is key for successful rounding.

Rounding Rules

Rounding a number helps simplify complex numbers or adapt them for conventional understanding, such as currency. The rules for rounding to the nearest hundredth can be summarized in a few steps:

• Examine the digit immediately to the right of the identified rounding place (hundredths here).
• If this digit is 5 or higher, increase the hundredths digit by one.
• If this digit is lower than 5, leave the hundredths digit unchanged.
• After adjusting, remove any digits following the hundredths place.

In the example of 79.369, you look at the thousandths place, which is 9. Since it's greater than 5, you round up the number in the hundredths place from 6 to 7, making the rounded number 79.37. These rules make rounding procedures systematic and predictable.