Question

Round the following decimals to the nearest thousandth. 5.8333 ______

Short answer

5.833

Step-by-step solution

Identify the thousandth place

To round to the nearest thousandth, first locate the thousandth place in the number. In the number 5.8333, the digits are: - **5** is the unit place. - **8** is the tenths place. - **3** is the hundredths place. - The third '3' is the thousandths place.

Check the digit after the thousandth place

To round to the nearest thousandth, check the digit in the ten-thousandths place (the fourth place after the decimal point). Here, the digit is also 3.

Apply rounding rules

According to rounding rules, if the digit in the ten-thousandths place is 5 or greater, you round up the digit in the thousandths place by one. Otherwise, you leave the thousandth digit as it is. Since our digit is 3, which is less than 5, we keep the thousandths digit (which is 3) the same.

Write the rounded number

Since the thousandths digit remains unchanged, the number 5.8333 rounded to the nearest thousandth is 5.833.

Key concepts

Decimal Places

When we work with decimals, each number to the right of the decimal point occupies a certain "place," each decreasing in value as you move further to the right. Starting from the left:

• Right next to the decimal point is the tenths place.
• The next digit is in the hundredths place.
• The third position is the thousandths place.
• Continuing, every position follows a predictable pattern: tenths, hundredths, thousandths, ten-thousandths, etc.

In the number 5.8333, 5 represents the whole part (units), and the numbers 8, 3, 3, and 3 follow the decimal. We identify these as being in the tenths, hundredths, thousandths, and ten-thousandths places respectively. Understanding these places is crucial when rounding decimals, ensuring precision and clarity in mathematical problems.

Rounding Rules

Rounding decimals is a way to simplify numbers, making them easier to understand and use in calculations. The primary rule in rounding is based on the digit right after the one you’re rounding. For instance:

• If the digit immediately to the right of the place you're rounding is 5 or higher, you round up.
• If that digit is less than 5, you round down, or essentially leave the digit as it is.

Applying this to 5.8333, the goal is to round to the nearest thousandth. Look at the ten-thousandths place, which in this case is 3. Since 3 is less than 5, we do not round up, and the thousandths place remains 3.
This straightforward approach assures accuracy while keeping the result manageable.

Mathematics Concepts

Understanding how decimal places relate to mathematical concepts is fundamental. Decimals are part of the number system which allows more precision than whole numbers. In mathematics, decimal places are particularly crucial for:

• Statistical data where precision is important.
• Scientific calculations involving measurements and experiments.
• Financial calculations where accuracy is critical in currency transactions.

When performing operations or making adjustments, such as rounding, being aware of the decimal's place value can significantly affect outcomes. Rounding can help simplify the numbers making calculations easier, though there is a trade-off with precision.
This is why understanding and applying the rules correctly is essential for both precision and practical use in various fields such as science, engineering, and economics.