Problem 78 - Prealgebra

Question

Round 53.967 to the nearest tenth.

Step-by-Step Solution

Answer

53.967 rounds to 54.0 to the nearest tenth.

Step 1: Identify the Tenth Place

The tenth place is the first digit to the right of the decimal point. In 53.967, the tenth place is the digit 9.

Step 2: Look at the Next Digit

Determine which digit immediately follows the tenth place. In 53.967, the digit after the tenth place is 6.

Step 3: Apply the Rounding Rule

Since the digit next to the tenth place is 6, which is greater than 5, we round up the tenth place digit by one. Thus, the digit 9 becomes 10, which affects the whole number, changing it to 54.0.

Step 4: Final Answer

After rounding, the number 53.967 becomes 54.0 when rounded to the nearest tenth.

Key Concepts

Decimal Places

Decimal places are the digits that appear to the right of the decimal point in a number. Understanding decimal places is essential when you need to perform operations like rounding, adding, or subtracting decimals. This specificity gives numbers more precision, important in many fields such as science, engineering, and finance.

Decimal places help us determine the value represented. For instance:

• In the number 53.967, there are three decimal places.
• The first decimal place is the tenths place, the second is the hundredths place, and the third is the thousandths place.

This understanding allows us to identify which digit needs attention during rounding or other numerical adjustments.

Tenth Place

The tenth place is the first digit right after the decimal point. In the decimal number system, this digit represents tenths of a whole unit. For example, in the number 53.967, the tenth place is occupied by the digit 9.

Focusing on this place value is crucial when the task is to round to the nearest tenth. By identifying the tenth place:

• We know exactly which digit we are considering for rounding.
• This digit represents one-tenth of the whole number, significantly impacting the overall value when rounded.

Recognizing the tenth place is the first step in rounding numbers effectively.

Rounding Rule

Rounding numbers involves approximating a number to its nearest place value, based on certain rules. The rounding rule primarily focuses on the digit right after the place value you want to round to, known as the rounding digit. For rounding to the nearest tenth, this means looking at the hundredths place.

Here is a simple rule to follow:

• If the rounding digit is 5 or more, round up the value in the specified position.
• If the rounding digit is less than 5, keep the value in the specified position the same.

In the number 53.967, since the digit 6 in the hundredths place is greater than 5, we round up the tenth place 9 to a 10, resulting in 54.0. This process ensures that our number becomes simpler while maintaining a good approximation of its previous value.