Problem 24 - Calculate With Confidence

Question

Express the following decimals to the nearest hundredth. 1.427 ______

Step-by-Step Solution

Answer

1.43

Step 1: Identify the Decimal Place

The number given is 1.427. To round to the nearest hundredth, identify the first three decimal places: tenths (4), hundredths (2), and thousandths (7).

Step 2: Check the Thousandths Place

Look at the thousandths place, which is the third digit after the decimal. For 1.427, the digit in the thousandths place is 7.

Step 3: Determine Rounding Action

According to rounding rules, if the digit in the thousandths place is 5 or above, round up the digit in the hundredths place. Since 7 is greater than 5, we will round up.

Step 4: Perform Rounding

Round the digit in the hundredths place (2) up by 1, changing it to 3. Thus, the decimal 1.427 rounded to the nearest hundredth is 1.43.

Key Concepts

Nearest Hundredth

When rounding a decimal to the nearest hundredth, it’s important to understand what this means precisely. The term "hundredth" refers to the second digit to the right of the decimal point in a number. For example, in the number 1.427, the hundredth place is occupied by the digit '2'. Rounding to the nearest hundredth means adjusting this specific digit, potentially changing the values in the hundredth, while eliminating all other less significant digits. The ultimate goal is to provide a simpler representation of the number that maintains as much accuracy as possible, making calculations or interpretations easier to handle. Remember, understanding the placement of these digits is key to correctly rounding numbers.

Rounding Rules

Rounding numbers follows a set of standard rules. These are used to decide whether the digit in the place we are rounding to should stay the same or be increased by one. Here are the basic rounding rules:

• *If the digit immediately after the rounding place (in this case, the thousandths) is 5 or greater, you round up the digit in the hundredths place by 1.*
• *If the digit is less than 5, you leave the digit in the hundredths place unchanged.*

In the example of 1.427, the digit in the thousandths place is '7'. Since '7' is greater than '5', we apply the rule to round up. The digit '2' in the hundredths place increases to '3'. These rules ensure consistency and accuracy in mathematical calculations.

Place Value Identification

Identifying place value is a crucial skill in mathematics, particularly when working with decimals. Place value refers to the value that a digit holds based on its position relative to the decimal point. In the number 1.427:

• *The '4' is in the tenths place, meaning it represents four-tenths or 0.4.*
• *The '2' is in the hundredths place, representing two-hundredths or 0.02.*
• *The '7' is in the thousandths place, standing for seven-thousandths or 0.007.*

Understanding these positions helps us to correctly apply rounding rules and accurately perform mathematical operations. It's important because each digit has a multiplier based on its place, affecting the value it contributes to the overall number.

Mathematics Education

Grasping the concepts of decimal rounding is a fundamental part of mathematics education. This topic touches on several foundational math skills, including understanding decimals, place value identification, and the application of rounding rules. Teaching these concepts effectively involves clear explanations and practice examples.

Math education often uses interactive methods such as:

• Breaking down complex processes into manageable steps.
• Utilizing visual aids to represent the placement and rounding of decimal numbers.
• Engaging students with practical problem-solving exercises.

This approach ensures students build a robust understanding, allowing them to apply these skills in various real-world contexts, like financial literacy, measurement, and scientific calculations. The focus should always be on making math approachable and applicable.