Problem 11 - Algebra 1: Concepts and Skills

Question

Round to the nearest tenth. $$ 56.068 $$

Step-by-Step Solution

Answer

The number \(56.068\) rounded to the nearest tenth is \(56.1\).

Step 1: Identify the Tenth Place

In the decimal number \(56.068\), the tenth place is filled by \(0\), the digit immediately after the decimal point.

Step 2: Check the Next Decimal Place

After identifying the tenth place, check the digit in the hundredth place. Here, it is \(6\). If this digit is \(5\) or greater, round up the tenth place.

Step 3: Round the Number

As the hundredth place value is \(6\), which is greater than \(5\), rounding the tenth place digit \(0\) up by one. The result is \(56.1\).

Key Concepts

Tenth Place

When dealing with decimal numbers, the tenth place holds a crucial role in rounding. This place is the first position immediately to the right of the decimal point. To identify it, simply locate the first digit that follows the decimal point. For example, in the decimal number 56.068, the tenth place is occupied by the digit 0. Understanding the tenth place is essential, as it sets the base for rounding decisions in decimal numbers.

Rounding typically affects the tenth place when deciding how a number should be adjusted to reflect a simpler or more approximate value. Whether it remains the same or increases depends on the digits that follow.

Hundredth Place

The hundredth place is the second position to the right of the decimal point, directly following the tenth place. In the number 56.068, you will find the number 6 sitting in the hundredth place. This placement is key to rounding decisions for the tenth place.

The rule for rounding relies significantly on the digit found here. If the digit in the hundredth place is 5 or greater, the tenth place gets rounded up. If it is 4 or lower, the tenth place remains unchanged. For our example, since the digit is 6 (which is greater than 5), we know we will round up.

Decimal Number Rounding

The process of decimal number rounding aims to simplify a number while maintaining its approximate value. This can make it easier to use in calculations or discussions. To round a decimal number, first, you'll need to identify the place you are rounding to, such as the tenth or hundredth place, and then look at the next digit to decide how to adjust.

For example, if rounding 56.068 to the nearest tenth, you check the hundredth place, which is 6. As 6 is greater than 5, you increase the tenth place digit by 1. Thus, 56.068 rounds off to 56.1.

• Identify the place you are rounding to
• Check the next digit
• Apply the rounding rule: 5 or greater rounds up, 4 or less stays the same
• Adjust the digit in the designated rounding place accordingly

The rounding rules help standardize how numbers are simplified while ensuring useful precision.