Problem 41 - Algebra A Combined Function

Question

Round each decimal to the given place value. $$ 0.234 \text { , nearest hundredth } $$

Step-by-Step Solution

Answer

0.234 rounded to the nearest hundredth is 0.23.

Step 1: Identify the hundredth place

In the number 0.234, identify the digits: 2 is in the tenths place, 3 is in the hundredths place, and 4 is in the thousandths place. Focus on the digit in the hundredths place, which is 3.

Step 2: Locate the digit to the right

Look at the digit to the right of the hundredth place, which is in the thousandths position. In 0.234, the digit in the thousandths place is 4.

Step 3: Determine rounding action

Since the digit to the right is 4 (which is less than 5), we do not round up the hundredth place digit but keep it the same.

Step 4: Write the rounded value

After deciding not to round up, the digit in the hundredth place remains 3. Thus, 0.234 rounded to the nearest hundredth is 0.23.

Key Concepts

Place Value

Understanding place value is crucial when rounding decimals. Place value tells us the value of a digit based on its position within a number. For example, in the decimal number 0.234:

• The digit 0 is in the units place.
• The digit 2 is in the tenths place.
• The digit 3 is in the hundredths place.
• The digit 4 is in the thousandths place.

Each place has a value ten times smaller as you move to the right. This system helps us pinpoint which digit to focus on when rounding. Recognizing these places lets you accurately change numbers to a required decimal precision. Remember, each step to the right after the decimal makes the number smaller relative to the whole.

Nearest Hundredth

When rounding to the nearest hundredth, you're dealing with the second digit after the decimal point. To successfully round to the nearest hundredth, follow these steps:

• Identify the digit in the hundredths place.
• In the number 0.234, the digit in the hundredths place is 3.
• Look at the digit to the right, which is in the thousandths place.

The digit to the right determines if you round the hundredths place up or keep it the same. If the digit is 5 or more, round up. If it is 4 or less, keep the digit the same. In our example, the digit 4 in the thousandths place leads to keeping the digit 3 unchanged. Therefore, 0.234 rounds down to 0.23 when rounded to the nearest hundredth. Practice helps in quickly identifying these positions and making rounding decisions effortlessly.

Thousandths Place

The thousandths place plays a crucial role when rounding to the nearest hundredth. Although it's the third place after the decimal, understanding its influence is essential. For 0.234:

• The thousandths place is occupied by the digit 4.

Why does the thousandths place matter? This digit dictates whether the hundredths place stays as it is or rounds up. If it's less than 5, as in our case, the digit in the hundredths place remains the same. As such, 0.234 becomes 0.23 when rounded.
Understanding the thousandths place is vital, especially if working with more precise measurements in subjects like science or finance, where accuracy is crucial. A minor digit can sometimes influence the broader outcome significantly, depending on the context.