Problem 65 - Prealgebra

Question

Complete the following table. $$\begin{array}{|c|c|c|c|} \hline \text {} & \text {} & \text { Round to the Nearest } & \text {} & \text {} \\ \text {Number} & \text { Whole Number } & \text { Tenth } & \text { Hundredth } & \text { Thousand } \\ \hline 2,789.3241 \\ \hline \end{array}$$

Step-by-Step Solution

Answer

2,789 to nearest whole, 2,789.3 to nearest tenth, 2,789.32 to nearest hundredth, 2,789.324 to nearest thousand.

Step 1: Understand the Task

We are given a number, 2,789.3241, and asked to round it to the nearest whole number, tenth, hundredth, and thousand.

Step 2: Rounding to the Nearest Whole Number

To round to the nearest whole number, look at the digit in the tenths place (3 in this case). Since 3 is less than 5, the number is rounded down. Therefore, 2,789.3241 rounded to the nearest whole number is 2,789.

Step 3: Rounding to the Nearest Tenth

To round to the nearest tenth, look at the digit in the hundredths place (2 in this case). Since 2 is less than 5, it rounds down. Therefore, 2,789.3241 rounded to the nearest tenth is 2,789.3.

Step 4: Rounding to the Nearest Hundredth

To round to the nearest hundredth, look at the digit in the thousandths place (4 in this case). Since 4 is less than 5, it rounds down. Therefore, 2,789.3241 rounded to the nearest hundredth is 2,789.32.

Step 5: Complete the Table

Fill in the table with the rounded values: \(\begin{array}{|c|c|c|c|c|} \hline \text{Number} & \text{Whole Number} & \text{Tenth} & \text{Hundredth} & \text{Thousand} \ \hline 2,789.3241 & 2,789 & 2,789.3 & 2,789.32 & 2,789.324 \ \hline \end{array}\)

Key Concepts

Understanding Whole Numbers

Whole numbers are the simplest type of numbers you can work with. They include all the numbers from zero upwards, without any fractions or decimals. These numbers are what we use to count objects: for example, 0, 1, 2, 3, and so on.
When rounding a decimal number like 2,789.3241 to the nearest whole number, we look at the first digit after the decimal point (which is called the tenths place). If this digit is 5 or more, we round the whole number part up by one. If it is less than 5, we keep the whole number the same. In our example, the tenths digit is 3, so the nearest whole number is 2,789.

Decoding Decimal Places

Decimal places refer to the digits that come after the decimal point. They allow us to express numbers that are not whole, providing finer precision. In the number 2,789.3241, there are four decimal places: 3, 2, 4, and 1. Each decimal place represents a fraction of a whole.
Understanding each place value is key when rounding.

• The first decimal place (tenths) is 3.
• The second (hundredths) is 2.
• The third (thousandths) is 4.

These digits help us determine how to round the number, depending on which decimal place we are interested in.

Place Value and Its Importance

Place value refers to the value of each digit in a number, depending on its position. This is true for both whole numbers and decimals. In the number 2,789.3241, each digit has a different place value. For instance, the digit 9 in 2,789 is in the units (or ones) place, while 3 is in the tenths place after the decimal.
Understanding place value is crucial for rounding because it helps you determine which digit to consider and adjust. The place value tells you what each digit represents, allowing you to accurately round numbers to the desired precision. For example, when rounding to the nearest tenth, the hundredths place (second decimal place) determines if the tenths place rounds up or stays the same.

Mastering Rounding Rules

Rounding rules are simple guidelines we use to adjust numbers to a desired degree of precision. The basic rounding rule is:

• If the digit immediately after the desired place is 5 or more, you round up.
• If it is less than 5, you round down by keeping the number the same, but dropping the additional decimals.

For rounding the number 2,789.3241:

• To round to the nearest whole number, check the tenths place (3). Since it's less than 5, the whole number is 2,789.
• To round to the nearest tenth, look at the hundredths place (2). Since it's less than 5, the result is 2,789.3.
• To round to the nearest hundredth, check the thousandths place (4). Again, less than 5, making it 2,789.32.

By applying these rules, you can accurately round numbers to the specified precision you need.