Problem 25 - Calculate With Confidence

Question

Express the following decimals to the nearest hundredth. 0.147 ______

Step-by-Step Solution

Answer

0.15

Step 1: Understand the Problem

The task is to round the given decimal number 0.147 to the nearest hundredth. The hundredth place is the second digit to the right of the decimal point.

Step 2: Identify Key Values

The number given is 0.147. The hundredth digit is 4, and the thousandth digit (which is the next digit) is 7.

Step 3: Apply Rounding Rule

In rounding, if the digit in the place to be rounded is followed by 5 or more, it is rounded up. Since the thousandth digit is 7, which is more than 5, we must round the hundredth digit up.

Step 4: Perform the Rounding

Given 0.147, change the hundredth digit from 4 to 5 because the thousandth digit is 7.

Step 5: Express the Rounded Number

The original number 0.147 rounded to the nearest hundredth is 0.15.

Key Concepts

Decimal Place Value

Understanding the concept of decimal place value is crucial in mathematics. When dealing with decimals, each digit holds a specific position and thus a specific value based on its placement.
The first position to the right of the decimal point is the tenths place, followed by the hundredths, thousandths, and so on. Each step further to the right represents a division by ten.
Decimals allow for a more precise representation of fractions, and understanding their place value helps in performing tasks like addition, subtraction, and rounding. This system allows for a structured approach to handling numbers beyond whole integers. It helps identify how much each digit contributes to the overall value of the number.

Hundredths Place

The hundredths place is significant when rounding decimals. It is the second digit to the right of the decimal point. This digit tells us the number of hundredths in a decimal.
In the context of rounding a decimal number, like 0.147, this digit plays a major role in determining how the number will be rounded.
Knowing which digit occupies the hundredths place allows you to decide whether that digit stays the same or gets rounded up based on the following number, known as the rounding digit. This precision is helpful in contexts where exact numbers are not necessary but an approximation is sufficient, like in financial calculations.

Rounding Rules

Rounding decimals involves applying certain rules to make numbers easier to work with. The main rule for rounding is to look at the digit immediately following the one you wish to round.

• If that digit is 5 or greater, you increase the rounding digit by one.
• If it is less than 5, you leave the rounding digit unchanged.

For example, in the decimal 0.147, the digit after the hundredths place (4) is 7, so we round up, making it 0.15. Adhering to these rounding rules helps provide a consistent and reliable way to approximate numbers for easier calculation and analysis.

Mathematics Education

Mathematics education provides the foundational skills and understanding required for applying mathematical principles in everyday life and professional settings. Learning to round decimals, for instance, is not just an isolated skill but part of a larger set of arithmetic operations taught early on.
Teaching students how to confidently handle numbers, including decimals, builds their competence in problem-solving and analytical thinking. Rounding is applied in various real-world situations, such as estimating costs or converting measurements.
Educators aim to make students comfortable with these practices, ensuring they are well-prepared for future encounters with numbers, whether in advanced mathematics or daily activities.