Question

Round the following decimals to the nearest thousandth. 7.8393 ______

Short answer

7.839

Step-by-step solution

Identify the Thousandth Place

First, locate the thousandth place in the decimal number. In 7.8393, the digits are arranged as follows: - 7 (ones) - 8 (tenths) - 3 (hundredths) - 9 (thousandths) The 9 is in the thousandth position.

Look at the Next Digit

The next step is to check the digit immediately following the thousandth place, which is used to determine whether to round up or stay the same. In the decimal 7.8393, the digit after the thousandth place is 3 (ten-thousandths).

Apply Rounding Rule

According to rounding rules, if the digit after the thousandth position is 5 or greater, you round up the thousandth position. If it is less than 5, you keep the thousandth position digit as it is. Since the next digit is 3, which is less than 5, the 9 in the thousandth position stays the same.

Write the Rounded Number

Finally, rewrite the number with only up to the thousandth position, removing all digits after it. For 7.8393, the rounded number to the nearest thousandth is 7.839.

Key concepts

Thousandth Place

Understanding decimal places is crucial when learning about rounding. The thousandth place is the third position to the right of the decimal point. When rounding a number to the nearest thousandth, it's important to identify this position correctly. Let's break it down with an example number: 7.8393. In this number, the places are:

• 7 in the ones position
• 8 in the tenths position
• 3 in the hundredths position
• 9 in the thousandths position

This identification allows you to focus on the digits needed for rounding. Picking the right digit to assess is half the battle in making sure rounding is accurate, so take your time when counting over the decimal places.

Rounding Rules

Rounding requires applying specific rules to adjust a number to its nearest simple form. These rules help turn complex numbers into more manageable figures.
When rounding to the nearest thousandth, the digit right after the thousandth place (the ten-thousandths digit) is crucial. Based on this digit, you decide whether to round up or leave the number as it is. Here are the basic rounding rules:

• If the next digit (right after the thousandth place) is 5 or more, you increase the thousandth digit by one. This is called "rounding up."
• If the next digit is less than 5, you keep the thousandth digit the same. This is sometimes called "rounding down" or "keeping the same."

In our example of 7.8393, the digit after the thousandths place is 3, which is less than 5. Therefore, the thousandth place doesn't change and the rounded number becomes 7.839.

Decimal Fractions

Decimals are a key part of everyday mathematics, widely used in measurements, money, and several other areas. Decimal fractions represent parts of a whole and are expressed in tenths, hundredths, thousandths, and so on. For instance, in 7.8393, 8393 represents 8393 parts of ten thousand. This is what makes decimals flexible and practical in showing precise values, as they can extend infinitely.It's important to understand how these decimals align and differ from traditional fractions. While a fraction like \(\frac{8393}{10000}\) may seem complex, the decimal 7.8393 shows the same value in a format that's easier to grasp visually and computationally. Through rounding, decimal fractions become simpler, without losing their essential value, helping us make real-world calculations efficient and accurate.