Problem 58 - Fundamentals of Mathematics

Question

For the following problems, perform the additions and round to the nearest hundred. $$ \begin{array}{r} 92 \\ 48 \\ \hline \end{array} $$

Step-by-Step Solution

Answer

The sum is 140, rounded to the nearest hundred is 100.

Step 1: Add the Numbers

First, we need to add the numbers 92 and 48 together. To do this, perform the addition: \[ 92 + 48 = 140 \].

Step 2: Determine the Rounding Increment

Next, we look at the hundreds place in the number 140 to determine what to round to. Since we are rounding to the nearest hundred, this increment will be 100.

Step 3: Assess the Tens Digit

After performing the addition, we have the number 140. To decide how to round, we check the tens digit of 140. The tens digit is 4, which is less than 5.

Step 4: Round Down

Since the tens digit of 140 is less than 5, we round 140 down to the nearest hundred. Therefore, 140 becomes 100 when rounded to the nearest hundred.

Key Concepts

Addition of Numbers

Adding numbers is one of the fundamental operations in arithmetic. It is the process of calculating the total or sum of two or more numbers. To add numbers, line them up vertically so that each digit falls into the correct column according to its place value (such as ones, tens, hundreds). Then, start adding from the rightmost column (ones) and move towards the left, carrying over any extra value if a column sums up to 10 or more.
For example, with the numbers 92 and 48:

• In the ones column, add 2 and 8, which equals 10. Write down 0 and carry over 1 to the tens column.
• In the tens column, add 9 and 4, then add the carryover 1, resulting in 14. Write down 4 and carry over 1 to the hundreds, or in this case, factor it into the final sum.

You will get a total of 140 as the sum of 92 and 48. This demonstrates how to sum digits appropriately across different columns, ensuring an accurate total.

Place Value

Understanding place value is crucial when performing addition or rounding numbers. Every digit in a number has a place value, which determines its value based on its position. Moving from right to left in a number, you have the ones place, tens place, hundreds place, and so on.

For example, in the number 140:

• The digit 0 is in the ones place, meaning its value is 0.
• The digit 4 is in the tens place, meaning its value is actually 40 (4 times 10).
• The digit 1 is in the hundreds place, meaning its value is 100.

Place value helps inform how we add and round numbers by showing the significance of each digit in determining the number's total worth. It is the backbone of performing operations like addition or rounding since we rely on knowing where each digit stands in the number hierarchy.

Number Rounding Rules

Rounding numbers is a method to simplify them, making them easier to work with in estimations or where precision is not incredibly crucial. When rounding, you adjust the digits of a number up or down to a specified place value, such as tens, hundreds, or thousands, based on certain rules.

To round a number, you:

• Identify which place value you are rounding to. In this case, the nearest hundred.
• Look at the digit immediately to the right of the place value you're rounding to—this tells you whether to round up or down.

Using 140 as an example:

• The hundreds place is 1.
• The next digit, in the tens place, is 4. Since 4 is less than 5, you round down.
• Hence, 140 rounded to the nearest hundred is 100.

These rounding rules help make figures simpler, often essential in everyday calculations or estimates where an exact number isn't necessary.