Problem 67 - Prealgebra

Question

Complete the following table. $$\begin{array}{|c|c|c|c|} \hline \text {} & \text {} & \text { Round to the Nearest } & \text {} & \text {} \\ \text {Number} & \text { Whole Number } & \text { Tenth } & \text { Hundredth } & \text { Thousand } \\ \hline 99.9999 \\ \hline \end{array}$$

Step-by-Step Solution

Answer

Whole: 100, Tenth: 100.0, Hundredth: 100.00

Step 1: Round to the Nearest Whole Number

The whole number is the number without any decimal points. To round 99.9999 to the nearest whole number, you need to look at the digit to the right of the decimal point (9 in this case). Since it is greater than or equal to 5, round up the whole number. Hence, 99.9999 rounded to the nearest whole number is 100.

Step 2: Round to the Nearest Tenth

To round to the nearest tenth, consider the first digit after the decimal point, which is 9, and the digit after it, which is 9. Since the next digit is 5 or greater, increase the tenth value by 1. Thus, 99.9999 rounded to the nearest tenth is 100.0.

Step 3: Round to the Nearest Hundredth

To round 99.9999 to the nearest hundredth, look at the second decimal digit (9) and the digit immediately following it (another 9). Again, since the next digit is 5 or greater, increment the hundredth place by 1. Therefore, 99.9999 rounded to the nearest hundredth is 100.00.

Step 4: Conclusion: Fill in the Table

Based on the rounding calculations:- Nearest Whole Number: 100- Nearest Tenth: 100.0- Nearest Hundredth: 100.00The completed table is:\[\begin{array}{|c|c|c|c|}\hline\text{Number} & \text{Whole Number} & \text{Tenth} & \text{Hundredth} \\hline99.9999 & 100 & 100.0 & 100.00 \\hline\end{array}\]

Key Concepts

Whole Numbers

Whole numbers are those that do not have any fractional or decimal component. They are just the complete units without any parts or decimal places involved. When you're thinking about rounding to whole numbers, you're simply asking, "what is the closest full unit to this number?" For instance, take the number 99.9999; the closest whole number is simply 100.
To determine this, look at the digit immediately after the decimal point. If it's 5 or more, you round up; if it's less than 5, you round down. In our case, 99.9999 is rounded to 100 because the first digit after the decimal, which is 9, requires rounding up.

Decimal Places

Decimal places refer to the numbers that come after the decimal point in a number. These decimal places can help us express numbers more precisely. When you hear the term "decimal place," it indicates the specific position of a digit in a number to the right of the decimal point.
In 99.9999, the first decimal place is 9, the second is also 9, and so on. Each position holds a place value and each sequential place to the right is a tenth, hundredth, thousandth, and so forth. Becoming comfortable with these places is crucial when you're trying to round numbers, whether to tenths, hundredths, or even thousandths.

Nearest Tenth

Rounding to the nearest tenth involves focusing on the first digit that comes after the decimal point, otherwise known as the tenths place. The goal here is to decide if the tenths digit should stay the same or be rounded up, based on the value of the digit in the hundredths place (the next digit to the right).
For example, when rounding 99.9999 to the nearest tenth, we start by looking at the first decimal digit: 9. We then check the next digit (also a 9). Since this is 5 or greater, the tenths digit rounds up from 9 to 10, which alters the number to 100.0. This decision is straightforward—just remember to check one digit beyond the targeted one to make the correct rounding decision.

Nearest Hundredth

To round a number to the nearest hundredth, you first look at the second digit after the decimal point, which is the hundredths place. Then, check the digit immediately following it, which is the thousandths place. This decision point will tell you if you need to round up or stay the same.
Take 99.9999, for instance. The hundredths place is the second 9. The next digit, another 9, is 5 or more, indicating the need to round up the hundredths place by one. The result is 100.00. By paying attention to the placement and value of decimal digits, you'll consistently round to the nearest hundredth correctly.