Problem 80 - Prealgebra

Question

Round 49.397 to the nearest hundredth.

Step-by-Step Solution

Answer

49.40

Step 1: Identify the Hundredth Place

The hundredth place in a number is the second digit to the right of the decimal point. In the number 49.397, this digit is 9.

Step 2: Identify the Next Digit

To determine whether to round up or keep the digit as is, look at the digit immediately following the hundredth place. In this case, it is the digit 7.

Step 3: Apply Rounding Rule

The rule for rounding is: if the next digit (after the place value you are rounding to) is 5 or greater, round up the digit in the hundredth place. Since the digit 7 is greater than 5, we will increase the hundredth place digit by 1.

Step 4: Perform the Rounding

Increase the hundredth place digit from 9 to 10. Since 10 is not a single digit, this causes an overflow to the next digit to the left, increasing it as well. Thus, 49.397 becomes 49.40 after rounding.

Step 5: Write the Final Answer

The number 49.397 rounded to the nearest hundredth is 49.40.

Key Concepts

Understanding the Hundredth Place

To round a number to the nearest hundredth, you first need to identify the hundredth place. This specific place value is crucial as it determines how your final number will look after rounding.
The hundredth place is the second digit situated to the right of the decimal point. In simpler terms, if you look at a number such as 49.397, you would identify the first digit after the decimal (3) as the tenth place, and the second digit (9) as the hundredth place. This place value tells us how precise our number is.
Remember, every digit to the right of the decimal has its own place value. The decimal point itself acts like a barrier separating whole numbers from their fractional counterparts.
Identifying these place values is essential. Without knowing the hundredth place, rounding would be nearly impossible.

Grasping Rounding Rules

Rounding is a method to simplify numbers while keeping them fairly close to what they originally were. It’s almost like tidying up a number. Here's how you can apply rounding rules effectively.
The basic rule for rounding is quite straightforward:

• Look at the digit immediately after the one you are rounding to.
• If this digit is 5 or greater, round up by adding one to the targeted digit.
• If it is less than 5, leave the digit as is.

For example, in the number 49.397, you want to round to the nearest hundredth. Look at the hundredth place (9), then at the next digit (7). Since 7 is greater than 5, you will round up the 9 to 10.
But there's a little twist, because rounding 9 up to 10 means you have to manage the 'overflow', making the number 49.40 instead.

Decoding Place Value

Place value is the value of where a digit is placed in a number, and understanding this can greatly clarify the process of rounding and calculating.
Each position in a number is ten times higher than the one to its right. For a number like 49.397:

• The digit 4 is in the tens place, meaning it represents 40.
• The digit 9 is in the units or ones place, adding up to 9.
• The 3 is in the tenths place, just after the decimal, which is 0.3.
• The 9, seen in the hundredths place, represents 0.09.
• And finally, the 7 stands in the thousandths place, or 0.007.

Knowing these positions makes it clear how each affects the value of the whole number. By comprehending place value, you can easily understand how different digits impact the number's size and how rounding changes these numerical landscapes.