Question

Round the following decimals to the nearest thousandth. 4.2475 ______

Short answer

4.2475 rounds to 4.248.

Step-by-step solution

Identify the Thousandth Place

The thousandth place is the third digit to the right of the decimal point. In the number 4.2475, the digit in the thousandth place is 7.

Identify the Next Digit

Look at the digit to the immediate right of the thousandth place to decide how to round. In this case, the digit after 7 in 4.2475 is 5.

Apply Rounding Rule

If the digit immediately after the thousandth place is 5 or greater, add 1 to the thousandth place digit. The digit is 5, which means the thousandth place digit 7 should be increased by 1.

Adjust the Number

Change the last three digits based on the rounding. The number 4.2475 rounds to 4.248 after increasing the thousandth place digit by 1.

Key concepts

Understanding the Thousandths Place

When dealing with decimal numbers, understanding the role each digit plays is crucial. The thousandths place is located as the third digit to the right of the decimal point.
The first digit immediately to the right of the decimal is known as the tenths place, the second is the hundredths, and the third is the thousandths.
For example, in the number 4.2475, the '4' is in the tenths place, the '2' is in the hundredths place, and '7' is in the thousandths place.

• This places significantly determines the precision of a decimal number value.

It's important to be able to quickly identify this place when rounding is required, as it serves as the primary location where changes will happen during the process of rounding to the nearest thousandth.

Mastering Rounding Rules

Rounding numbers follows a set of specific rules that ensure consistency and accuracy. The guiding principle in decimal rounding is determining whether the next digit after your place of interest (thousandths, in this case) will "round up" or stay the same.
Here's a concise way to remember these rules:

• If the digit is 5 or greater, round the digit in your place of interest up by one.
• If the digit is less than 5, keep the digit in your place of interest the same.

Applying these rules to our example, 4.2475, since the digit following the thousandths place (which is '7') is '5', we round the 7 up to 8.

This turns the number into 4.248. Mastering these simple rules helps ensure that your rounding is both quick and accurate.

Exploring Decimal Place Value

Decimal place value operates on a positional value system similar to whole numbers, but crucially, to the right of the decimal point.
Each position indicates a fractional part of one whole.

• The first position to the right is the tenths, representing one-tenth of a whole.
• The second position is the hundredths, representing one hundredth of a whole.
• The third is the thousandths, representing one thousandth of a whole.

This idea of place value is essential in mathematics because it explains how we can fractionally represent numbers and perform operations like rounding.
For the number 4.2475, knowing these place values helps us understand how each movement can impact the value of the decimal.
Always remember, understanding place values can help you not only in rounding but also in addition, subtraction, and comparing decimals effectively.