Problem 77 - Algebra 1: Concepts and Skills

Question

Round to the nearest cent. $$ \$ 8.357 $$

Step-by-Step Solution

Answer

\$8.36

Step 1: Identify decimal place

Locate the second decimal place (the hundredths), which represents cents. In this case, it's 5.

Step 2: Check the third decimal place

Check the number in the third decimal place (the thousandths), which is 7.

Step 3: Determine if rounding up or down

If the number in the third decimal place is 5 or above, round the number in the second decimal place up by one. If it's 4 or below, leave it as is. In this case, because 7 is greater than 5, round the number in the cents place up by one to become 6.

Key Concepts

Decimal Places

Decimal places are crucial when it comes to precisely understanding and working with numbers, especially in contexts like money where accuracy is important. A decimal place is the position of a number to the right of the decimal point. Each position has a specific value:

• The first position is the tenths place.
• The second position is the hundredths place, which is important for rounding currency because it represents cents.
• The third position is the thousandths place.

This understanding helps us discuss terms like rounding to the nearest cent, which involves the first two decimal places.

Rounding Rules

Rounding helps make numbers easier to work with by simplifying them. To round accurately, you need to know the basic rules:

• Identify the digit in the place to which you are rounding. For cents, this is the second decimal place or the hundredths place.
• Look at the digit to the right of it. This is crucial as it determines whether you round up or stay the same.
• If the digit is 5 or more, increase the identified digit by one.
• If it is less than 5, leave the identified digit unchanged.

In practice, for a number like $8.357$, you find that the third decimal place is a 7, which means you round the second decimal place up from 5 to 6, giving you $8.36 as the rounded result.

Math Skills

Enhancing math skills, particularly in rounding, benefits from practice and understanding the broader context of each step. Here's how to strengthen those skills:

• Practice identifying the decimal places quickly and accurately. This helps in speeding up the process of rounding.
• Understand the importance of numbers and their values. Knowing why and when to round can help make learning purposeful, especially with financial mathematics.
• Utilize real-world examples, such as calculating the total cost of items when shopping, to make math skills feel relevant.
• Remember that like any math skill, success in rounding comes from practicing with guided examples until the process feels natural.

Rounding isn't just a classroom exercise; it's a math skill that's applicable in everyday life, helping you work with numbers more effectively.