Problem 71 - Prealgebra

Question

Round 71.2427 to the nearest thousandth.

Step-by-Step Solution

Answer

71.243

Step 1: Identify the thousandth place

In the number 71.2427, the thousandth place is the third digit to the right of the decimal point, which is 2.

Step 2: Identify the digit to the right of the thousandth place

The digit to the right of the thousandth place is in the ten-thousandth place, which is 7 in 71.2427.

Step 3: Decide whether to round up or stay the same

Since the digit in the ten-thousandth place (7) is 5 or more, we round up the number in the thousandth place. Therefore, the 2 becomes a 3.

Step 4: Write the rounded number

After rounding, the number becomes 71.243.

Key Concepts

Understanding the Thousandth Place

Decimals are a way of expressing numbers that lie between whole numbers. They use place values to represent the fractions between these numbers. One such place value is the thousandth place. In a decimal number, each digit has a specific position. The first digit to the right of the decimal point is the tenths place. The second is the hundredths place, and the third is the thousandths place.

For example, in the number 71.2427, the decimal portion is 2427. Here:

• The 2 in the first position is in the tenths place.
• The 4 in the second position is in the hundredths place.
• The 2 in the third position is in the thousandths place.

This shows that the thousandth place is the third position to the right of the decimal point. It's crucial when rounding numbers, as it determines how precise a number is expressed.

What Are Decimal Places?

Decimal places are the positions of figures in a decimal, counting from the decimal point to the right. They help express values more accurately than whole numbers. Each position signifies a division by 10. The more decimal places a number has, the more precise it is. For instance:

• 0.1 has one decimal place.
• 0.01 has two decimal places.
• 0.001 has three decimal places.

In the context of our exercise, 71.2427 has four decimal places. These decimal places help us understand the exact value being represented. In practical terms, rounding helps manage these decimal places, especially when an exact value isn't necessary or useful, creating a balance between precision and simplicity.

Mastering Number Rounding Rules

Rounding is important for simplifying numbers while retaining as much accuracy as needed. The number rounding rules can help decide whether a digit should increase, decrease, or stay the same. When rounding a decimal number:

• Identify the decimal place you're rounding to.
• Look at the digit immediately to the right of that place.
• If this digit is 5 or greater, round the target place up by one.
• If it is less than 5, leave the target place unchanged.

In our exercise, we focused on rounding to the thousandth place in the number 71.2427. The digit in the ten-thousandth position is 7, which is greater than 5, so we round up the thousandth place from 2 to 3, resulting in 71.243. This rule ensures the rounded-off number remains as close to the original as possible.