Problem 78 - Algebra 1: Concepts and Skills

Question

Round to the nearest cent. $$ \$ 7.134 $$

Step-by-Step Solution

Answer

The number $7.134, rounded to the nearest cent, is $7.13.

Step 1: Identify the number to be rounded

The number to be rounded is 7.134. In this number, the cent place is the second decimal place, which is 3.

Step 2: Check the next decimal place

The next decimal place after the cent is 4. In rounding, when this number is 5 or more, we round up. And when it's less than 5, we stick with the current number. Since 4 is less than 5, we don't round up.

Step 3: Round to the nearest cent

Since we are not rounding up, the number rounded to the nearest cent is 7.13.

Key Concepts

Decimal Place Value

Understanding decimal place value is crucial for rounding numbers effectively. Decimals, unlike whole numbers, have places that represent fractions of a whole.
The first place to the right of the decimal point is called the tenths place, and the one after that is the hundredths place, often referred to as the 'cent' place when dealing with money.
The number 7.134 can be broken down as follows:

• 7 is in the whole number place, representing the number of whole units.
• 1 is in the tenths place; it's like having \(1/10\) of a whole unit.
• 3 is in the hundredths place, which is very important when rounding to the nearest cent.
• 4 is in the thousandths place, showing even finer detail but doesn’t always affect simple rounding.

Recognizing each digit’s place value helps in accurate rounding.

Rounding Rules

Rounding rules help us decide when to adjust a number. Simply put, if the digit to the right of the place you're rounding to is 5 or greater, you round up.
If it's less than 5, you leave the number as it is.

• Identify the rounding digit: In financial calculations, usually the hundredths place.
• Look at the next digit: If it’s 5 or more, increase the rounding digit by one.
• If it’s less than 5, the rounding digit remains unchanged.

For the example 7.134:

• The hundredths place is 3.
• Check the thousandths place, which is 4.
• Since 4 is less than 5, 3 stays the same.

Thus, rounding to the nearest cent gives us 7.13.

Mathematics Education

Mathematics education emphasizes understanding fundamental concepts such as rounding. Making these concepts clear through practical examples like money improves comprehension.
Students learn how to systematically approach problems, such as identifying relevant digits and applying rounding rules. This approach is beneficial not only in math classes but also in real-life money handling.
Eduation also covers:

• Problem-solving and logical thinking skills.
• Practical application of mathematics in everyday scenarios, like budgeting.
• Building confidence and accuracy in numerical calculations.

Understanding how to round numbers effectively, especially in financial contexts, is a valuable skill that enhances numeracy and promotes lifelong learning.