Problem 42 - Algebra A Combined Function

Question

Round each decimal to the given place value. $$ 0.452, \text { nearest hundredth } $$

Step-by-Step Solution

Answer

0.45

Step 1: Understanding Place Values

Firstly, identify the hundredths place in the decimal number. For the number 0.452, the hundredths place is occupied by the digit 5, which is the second digit to the right of the decimal point.

Step 2: Identifying the Rounding Digit

Next, look at the digit immediately to the right of the hundredths place to decide whether to round up or keep the same digit. In 0.452, this digit is 2.

Step 3: Applying Rounding Rules

Since the digit in question (2) is less than 5, we do not round up. According to rounding rules, if the digit is 4 or less, you leave the hundredths digit as it is.

Step 4: Write the Rounded Number

The rounded number to the nearest hundredth is therefore 0.45. Ensure that only two digits are present after the decimal point.

Key Concepts

Understanding the Hundredths Place

When working with decimals, one of the critical skills to master is understanding how to identify different place values. Place values help us determine which digit represents what part of the whole number. In the decimal system, the decimal point is a key feature: everything to the left represents whole numbers, and everything to the right represents fractions of whole numbers. The hundredths place is the second digit to the right of the decimal point.

• For example, in the number 0.452, the hundredths place is occupied by the digit 5.
• This position can be visualized by reading "tenths, hundredths, thousandths" as you move right from the decimal point.

Identifying the hundredths place accurately is important when performing tasks like rounding, as it determines what digit will be altered or kept.

Rounding Rules Simplified

Once you have identified the place value you are working with, the next step is to apply the rules of rounding. Rounding allows you to simplify numbers while maintaining their approximate value, which makes them easier to work with for estimation purposes. The basic rule of rounding depends on the number immediately following the digit in the place value that you are examining:

• If that digit is 5 or greater, round up the digit in the place you're rounding to.
• If it is less than 5, do not change the digit in the rounded place, leaving it the same.

For example, in rounding 0.452 to the nearest hundredth, you look at 2—the digit that follows the hundredths place (5).

• Since 2 is less than 5, the digit 5 stays the same.
• Thus, the rounded number remains at 0.45 after simplifying to two decimal places.

Remembering these simple rules will help you round any decimal correctly.

Mastering Place Value Identification

Place value identification is fundamental when dealing with numbers and especially important in understanding decimal numbers. Recognizing place values allows you to accurately work with digits regardless of where they are located in a number. Consider the number 0.452:

• The digit "4" is in the tenths place. It's the first digit to the right of the decimal point.
• The digit "5" resides in the hundredths place, being the second position to the right.
• Finally, "2" is in the thousandths place, which is the third position to the right.

Each digit's place has an associated value that decreases tenfold as you move to the right from the decimal. By identifying these values correctly:

• You set a strong foundation for rounding, addition, subtraction, and other arithmetic with decimals.
• Place values help track the precision needed in your calculations, ensuring accurate results in real-world scenarios like financial transactions, scientific measurements, or cooking recipes.

Once you understand place values, focusing on the relevant digits for your calculations becomes much simpler, whether it's for rounding or performing other operations.