Problem 43 - Calculate With Confidence

Question

Round the following decimals to the nearest thousandth. 7.8393 ___________

Step-by-Step Solution

Answer

7.839

Step 1: Identifying the Thousandth Place

Examine the given decimal, 7.8393, and locate the digit in the thousandth place. The thousandth place is the third digit to the right of the decimal point. In this case, it is the digit '9' in the number 7.8393.

Step 2: Checking the Next Digit

Look at the digit immediately to the right of the thousandth place to determine rounding. This digit is in the ten-thousandth place. In 7.8393, the digit in the ten-thousandth place is '3'.

Step 3: Applying Rounding Rules

Use the rounding rule: if the next digit (ten-thousandth place) is 5 or more, round up the thousandth place digit by 1. If it is less than 5, leave the thousandth place digit as it is. Since the ten-thousandth digit is '3', which is less than '5', we do not round up.

Step 4: Writing the Rounded Number

Based on the rounding rules, the number 7.8393 rounded to the nearest thousandth is 7.839.

Key Concepts

Understanding the Thousandth Place

When rounding decimals, knowing which digit represents the thousandth place is crucial. This place is three digits to the right of the decimal point.

For example, in the decimal number 7.8393, the number '9' occupies the thousandth place. Visualize the position by counting three numbers after the decimal point:

• First: '8' (tenth place)
• Second: '3' (hundredth place)
• Third: '9' (thousandth place)

This systematic approach helps locate the thousandth place swiftly.

Identifying the Decimal Point

The decimal point is essential in distinguishing between whole numbers and fractional parts. It separates the integer part of a number from its fractional part.

In the number 7.8393, the decimal point follows the '7'.

Think of the decimal point as a gateway:

• Numbers to the left ('7') count as whole numbers.
• Numbers to the right ('8393') count as decimals or fractions.

This distinction aids in navigating and pinpointing specific places such as the thousandth and ten-thousandth.

Mastering the Rounding Rules

Rounding rules guide us in simplifying decimals. The process mainly focuses on the digit right after the target place. In this context, if we target the thousandth place, we inspect the ten-thousandth place.

Here are the common rounding rules:

• If the digit in the ten-thousandth place is 5 or more, increase the thousandth place digit by 1.
• If the digit in the ten-thousandth place is less than 5, leave the thousandth place digit unchanged.

Applying these rules to 7.8393, the ten-thousandth digit '3' is less than '5,' so the thousandth digit '9' remains the same, resulting in 7.839.

The Role of the Ten-Thousandth Place

The ten-thousandth place is precisely the fourth digit to the right of the decimal point. It's pivotal in rounding as it dictates whether to round up or stay put.

In the number 7.8393, '3' is the digit occupying the ten-thousandth place. To comprehend its role, visualize the positions again:

• '8' in the tenth place
• '3' in the hundredth place
• '9' in the thousandth place
• '3' in the ten-thousandth place

Even though it seems less significant, this digit ensures precision in rounding processes.