Problem 39 - Algebra A Combined Function

Question

Round each decimal to the given place value. $$ 0.57 \text { , nearest tenth } $$

Step-by-Step Solution

Answer

0.6

Step 1: Identify the Tenths Place

In the decimal number 0.57, the digit in the tenths place is the first digit right after the decimal point. So, 5 is in the tenths place.

Step 2: Identify the Hundredths Place

Next to the tenths place is the hundredths place. In 0.57, the digit in the hundredths place is 7.

Step 3: Apply Rounding Rules

To round 0.57 to the nearest tenth, look at the hundredths place. If the digit in the hundredths place is 5 or greater, we round up the tenths place by 1. Since 7 is greater than 5, we will round up.

Step 4: Execute Rounding

Since the digit in the hundredths place (7) is greater than 5, increase the digit in the tenths place (5) by 1. This results in 0.6.

Key Concepts

Tenths Place

When you're working with decimals, understanding the tenths place is essential. The tenths place is the first digit that appears right after a decimal point in a number. It represents one-tenth of a whole number. For example, in the decimal \(0.57\), the digit \(5\) is in the tenths place.

This place value gives us an idea about how close the entire number is to the next whole number. Understanding how to identify the tenths place allows you to decide on how a number would change if rounded. For decimal numbers, starting with the tenths place sets the stage for all further calculations and rounding decisions.

Hundredths Place

After you identify the tenths place, the next digit to the right is the hundredths place. This represents one-hundredth of a whole number. In \(0.57\), the digit \(7\) resides in the hundredths place.

The role of the hundredths place is crucial when you need to round a number to the nearest tenth. Essentially, the digit in this position helps determine whether the tenths digit should stay the same or increase by one. Without a clear understanding of this place value, rounding accurately can become a challenge.

Rounding Rules

Rounding is an important technique used to approximate a number to its nearest place value, simplifying a number for easy understanding and use. Here are some basic rounding rules:

• If the digit in the place to the right of the place you are rounding to (in this case, the hundredths place for tenths rounding) is 5 or greater, you round up the digit in the target place (the tenths place).
• If the digit is less than 5, you keep the digit in the tenths place the same.

In the example \(0.57\), since the hundredths digit \(7\) is greater than \(5\), we round up \(5\) in the tenths place to \(6\). This rounding rule lets you quickly and accurately represent values with less precision without significantly altering their meaning.