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Chapter 1: Problem 548

Round each number to the nearest tenth. $$ 0.49 $$

Short Answer

Expert verified
0.5

Step by step solution

01

Identify the Tenths and Hundredths Places

First, identify the digit in the tenths place and the digit in the hundredths place. In the number 0.49, the tenths place is occupied by 4, and the hundredths place is occupied by 9.
02

Determine Rounding Up or Down

Look at the digit in the hundredths place to determine whether to round up or down. If the hundredths digit is 5 or greater, round up the tenths place by 1. If it is less than 5, keep the tenths place the same. Since the hundredths digit in 0.49 is 9, round up.
03

Perform the Rounding

Since 9 is greater than 5, add 1 to the tenths place digit. Therefore, 4 becomes 5. The number 0.49 rounded to the nearest tenth is 0.5.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Tenths Place
The tenths place is the first digit to the right of the decimal point in a number. In the number 0.49, the digit in the tenths place is 4. This place value plays a crucial role when we round numbers to the nearest tenth, as it's the digit that changes based on the value of the hundredths place.

The tenths place can be identified easily by looking at the decimal number. For instance, in the number 12.34, the digit 3 is in the tenths place. Knowing this helps us understand which digit we may need to adjust when rounding.

To round a number to the nearest tenth:
  • Locate the digit in the tenths place.
  • Check the digit in the hundredths place.
  • Decide whether to round the tenths digit up or keep it the same.
Hundredths Place
The hundredths place is the second digit to the right of the decimal point. In the number 0.49, that digit is 9. This digit is essential when rounding numbers because it determines whether we round up or down the tenths place.

For example, in the number 0.564, the hundredths place is occupied by the digit 6. This tells us if we should round the tenths place digit (5) up to 6 or keep it the same.

Here's how to easily identify and use the hundredths place in rounding:
  • Find the second digit to the right of the decimal point鈥攖his is the hundredths place.
  • Determine if it is 5 or greater to round up the tenths place.
  • If the digit is less than 5, the tenths place remains the same.
Rounding Rules
Rounding rules are essential guidelines that help us adjust numbers to a specified place value. In our case, we're focusing on rounding to the nearest tenth. Here鈥檚 a breakdown of the rounding rules:

1. Identify the place value you want to round to (e.g., tenths place).
2. Look at the digit immediately to the right of that place value (hundredths place).
3. If the digit in the hundredths place is 5 or greater, add 1 to the tenths place.
4. If it is less than 5, keep the tenths place the same.

For example, when rounding 0.49 to the nearest tenth:
  • First, identify that 4 is in the tenths place, and 9 is in the hundredths place.
  • Since 9 is greater than 5, you round the 4 in the tenths place up to 5.
  • Hence, 0.49 rounded to the nearest tenth becomes 0.5.

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