Problem 60 - Prealgebra

Question

Complete the following table. $$\begin{array}{|c|c|c|c|} \hline \text {} & \text {} & \text { Round to the Nearest } & \text {} & \text {} \\ \text {Number} & \text { Whole Number } & \text { Tenth } & \text { Hundredth } & \text { Thousand } \\ \hline 100.9256 \\ \hline \end{array}$$

Step-by-Step Solution

Answer

101 (Whole), 100.9 (Tenth), 100.93 (Hundredth), 100.926 (Thousandth).

Step 1: Round to the Nearest Whole Number

100.9256 rounded to the nearest whole number requires us to look at the digit in the tenths place. The digit is 9, which is 5 or more, so we round up the digit in the ones place from 0 to 1. Therefore, 100.9256 rounded to the nearest whole number is 101.

Step 2: Round to the Nearest Tenth

For rounding 100.9256 to the nearest tenth, examine the digit in the hundredths place, which is 2. Since this digit is less than 5, the tenths digit remains the same. Therefore, rounding to the nearest tenth gives us 100.9.

Step 3: Round to the Nearest Hundredth

To round 100.9256 to the nearest hundredth, look at the digit in the thousandths place, which is 5. Since it is 5 or more, we increase the digit in the hundredths place from 2 to 3. Therefore, the number rounded to the nearest hundredth is 100.93.

Step 4: Round to the Nearest Thousandth

Rounding 100.9256 to the nearest thousandth requires checking the next digit, which is beyond the thousandths place. The digit is 6, which is 5 or more, so we increase the digit in the thousandths place from 5 to 6. Thus, the number rounded to the nearest thousandth is 100.926.

Key Concepts

Whole Numbers

Whole numbers are the simplest form of numbers. They include all the numbers starting from zero and going up without including any fractions or decimals. They are non-negative integers such as 0, 1, 2, 3, and so forth.
Whole numbers do not have decimal or fractional parts. When you are asked to round a decimal to the nearest whole number, you are essentially trying to find the closest integer without considering any decimal part of the number.
For example, if you have the number 100.9256 and you need to round it to the nearest whole number, you look at the digit in the tenths place. Since it is 9, which is 5 or greater, you round up the integer part. This gives you 101 as the nearest whole number.

Decimal Places

Decimal places refer to the position of a number after the decimal point. They represent a fraction of a whole number and give us the precision of a number.
Let's break it down:

• The first place after the decimal point is the tenths place.
• The second place is the hundredths place.
• The third place is the thousandths place.

The more decimal places a number has, the more precise it is. For example, in 100.9256, the number 9 is in the tenths place, 2 is in the hundredths place, and so on. Each position represents a different level of precision when you round this number.

Place Value

Place value helps us understand the value of a digit in a number based on its position. It's crucial for rounding numbers correctly.
Here's a quick guide to understanding place values in decimals:

• Units place: where whole numbers reside (left of the decimal).
• Tenths place: the first place right after the decimal point.
• Hundredths place: the second digit after the decimal.
• Thousandths place: the third digit following the decimal.

A digit's place value determines its role in rounding. For instance, when rounding to the nearest hundredth, look at the thousandths place to decide whether to round up or keep the same hundredths value.

Rounding Rules

Rounding rules are guidelines that tell us how to round numbers to a desired level of precision. Understanding these rules is key when you need to simplify numbers without losing their value significantly.
The basic rules are:

• If the digit to the right of the place you are rounding to is less than 5, leave the digit at the rounding place unchanged.
• If the digit to the right is 5 or more, increase the digit in the rounding place by 1.

For example, when rounding 100.9256 to the nearest hundredth, look at the thousandths place (which is 5). Because 5 is a threshold for rounding up, the hundredths digit increases from 2 to 3. Knowing these rounding rules makes rounding numbers straightforward and accurate.