Problem 62 - Prealgebra

Question

Complete the following table. $$\begin{array}{|c|c|c|c|} \hline \text {} & \text {} & \text { Round to the Nearest } & \text {} & \text {} \\ \text {Number} & \text { Whole Number } & \text { Tenth } & \text { Hundredth } & \text { Thousand } \\ \hline 29.9876 \\ \hline \end{array}$$

Step-by-Step Solution

Answer

Whole number: 30; Tenth: 30.0; Hundredth: 29.99; Thousandth: 29.988.

Step 1: Round to Whole Number

Identify the whole number part and the tenths digit to determine rounding. The number is 29.9876, so the whole number is 29, and the tenths digit is 9 (because the decimal is more than .5, round up). Thus, 29.9876 rounded to the nearest whole number is 30.

Step 2: Round to the Nearest Tenth

Identify the tenths and hundredths digit to determine rounding. The tenths digit is 9, and the hundredths digit is 8. Since 8 is greater than 5, we round 9 up to 10, essentially increasing the whole number part, making it 30.0.

Step 3: Round to the Nearest Hundredth

Identify the hundredths and thousandths digit to determine rounding. The hundredths digit is 8, and the thousandths digit is 7. Since 7 is greater than 5, round 8 up to 9, resulting in 29.99.

Step 4: Round to the Nearest Thousandth

Identify the thousandths and ten-thousandths digit to determine rounding. The thousandths digit is 7, and the ten-thousandths digit is 6. Since 6 is greater than 5, round 7 up to 8, giving 29.988.

Key Concepts

Whole Number Rounding

Rounding to the nearest whole number means we aim to eliminate the decimal part entirely. To do this, we primarily examine the tenths place in the decimal. If the digit in the tenths place is 5 or greater, we round the entire number up. In contrast, if the tenths digit is less than 5, we keep the whole number part unchanged.

• For example, with the number 29.9876, the whole number is 29, and the tenths digit is 9.
• Since 9 is greater than 5, we round 29.9876 up to 30.

This simple rule helps us make approximate estimates more manageable.

Decimal Places

When we refer to decimal places, we are talking about the position of digits to the right of the decimal point in a number. Each position has a specific value:

• The first place is tenths.
• The second place is hundredths.
• The third place is thousandths.

Understanding decimal places is crucial for precision in rounding and helps us decide how much detail we want to preserve in a number, depending on the context.

Rounding Rules

Rounding rules dictate how we change a number's digits to make it easier to work with, while still keeping it close to its original value. The fundamental rule for rounding is simple:

• If the digit we are considering rounding is 5 or greater, increase the digit to the left by one.
• If the digit is less than 5, leave the digit to the left unchanged.

These rules apply whether we are rounding to whole numbers or specific decimal places, ensuring accuracy and consistency in mathematics.

Rounding to Tenth

Rounding to the nearest tenth involves examining the tenths and the subsequent hundredths digit. First, identify these two digits in the number. If the hundredths digit is 5 or more, round the tenths digit up.

For instance, take 29.9876:

• The tenths digit is 9.
• The hundredths digit is 8.

Since 8 is greater than 5, you increase 9 to 10, which rolls over to the next whole number, rounding 29.9876 to 30.0.

Rounding to Hundredth

When rounding to the nearest hundredth, examine the hundredths and thousandths digits. Look at the thousandths digit to decide on rounding the hundredths place.

Consider 29.9876:

• The hundredths digit is 8.
• The thousandths digit is 7.

Since 7 is more than 5, round the 8 up to 9. This makes 29.9876 become 29.99 at the hundredth decimal place, demonstrating how sharp attention to detail in decimals refines precision.

Rounding to Thousandth

Rounding to the nearest thousandth considers the thousandths and ten-thousandths digits. Pay attention to whether the ten-thousandths digit affects the rounding of the thousandths digit.

Looking at 29.9876:

• The thousandths digit is 7.
• The ten-thousandths digit is 6.

Since 6 is greater than 5, the 7 increases to 8, transforming the number into 29.988. Understanding this helps provide accuracy on detail-rich calculations.