Problem 72 - Prealgebra

Question

Round 59.2125 to the nearest thousandth.

Step-by-Step Solution

Answer

59.213

Step 1: Identify the thousandths place

The digit in the thousandths place of the number 59.2125 is the third digit to the right of the decimal point, which is 2.

Step 2: Look at the digit in the next smallest place

The digit in the ten-thousandths place, which is the fourth digit to the right of the decimal, is 5. This is the digit we will use to determine whether to round up or stay the same.

Step 3: Apply rounding rules

Since the digit in the ten-thousandths place is 5, we round the thousandths place up according to rounding rules. This means we add 1 to the thousandths place digit, changing it from 2 to 3.

Step 4: Write the final rounded number

After rounding, the digits after the thousandths place are removed, so the number 59.2125 rounded to the nearest thousandth is 59.213.

Key Concepts

Thousandths Place

When we talk about the thousandths place in a decimal number, we refer to a specific location relative to the decimal point. Imagine a decimal number like 59.2125. The digits after the decimal point are organized into different places: tenths, hundredths, thousandths, and so on.

• The first digit right after the decimal is the tenths place, which in our number is 2.
• The second digit is the hundredths place, which is 1.
• The third digit is the thousandths place, which is our main focus, and it is 2 in the number 59.2125.

Knowing the thousandths place is crucial when rounding to the nearest thousandth. To round correctly, we need to evaluate this position and consider the digits that follow for further accuracy.

Rounding Rules

Rounding numbers simplify them while keeping them close to the original value. When rounding to the nearest thousandth, the rules involve deciding whether the value in the thousandths place should stay the same or be adjusted. Here's how it works:

• Locate the digit right after the thousandths place; for 59.2125, it's the fourth digit, which is 5.
• Apply the rounding rules:
• If this following digit is 5 or more, increase the thousandths place by 1.
• If it's less than 5, keep the thousandths place as it is.

In our example, since the digit is 5, we add 1 to the 2 in the thousandths place, making it 3. Thus, 59.2125 becomes 59.213 after rounding.

Place Value

Understanding place value is a foundation of rounding and many other math concepts. Each digit in a number has a specific value based on its position. For decimals like 59.2125, here's a breakdown:

• The whole number part is to the left of the decimal, which is 59.
• To the right, the decimal places start with tenths, hundredths, then thousandths, each of which gets progressively smaller.
• The thousandths place is crucial when considering exactness in decimals, especially in contexts like measuring or financial calculations.

This framework allows us to accurately identify and manipulate digits for tasks like rounding, ensuring that our results are both precise and easy to understand.