Problem 11 - Fundamentals of Mathematics

Question

For the following problems, complete the table by rounding each number to the indicated positions. 199 $$ \begin{array}{|l|l|l|l|} \hline \text { hundred } & \text { thousand } & \text { ten thousand } & \text { million } \\ \hline & & & \\ \hline \end{array} $$

Step-by-Step Solution

Answer

200, 0, 0, 0

Step 1: Understanding the Place Values

The task is to round the number 199 to different named place values such as hundred, thousand, ten thousand, and million. By rounding, we adjust the number to the nearest value as per the place value specified.

Step 2: Rounding to the Nearest Hundred

The number 199 is already below the next hundred, which is 200, but since it is closest to 200, we round 199 up to 200. Thus, the number rounded to the nearest hundred is 200.

Step 3: Rounding to the Nearest Thousand

Since 199 is less than 1000, rounding to the nearest thousand results in the number being rounded down to zero. Therefore, to the nearest thousand, 199 rounds to 0.

Step 4: Rounding to the Nearest Ten Thousand

Once again, since 199 is significantly less than 10,000, it rounds down to zero when rounded to the nearest ten thousand. Therefore, 199 rounds to 0 when rounded to the nearest ten thousand.

Step 5: Rounding to the Nearest Million

For the nearest million, 199 is far less than 1,000,000. Thus, it also rounds down to zero. Therefore, to the nearest million, 199 rounds to 0.

Key Concepts

Place Value

Place value refers to the value a digit holds based on its position within a number. Each digit in a number has a place, such as ones, tens, hundreds, etc.
It's essential to understand that a number, like 199, consists of different digits:

• The digit '1' in 199 represents 100 because it is in the hundreds place.
• The digit '9' in the tens place represents 90.
• The second '9' in the ones place represents 9.

Knowing the place values helps us round the numbers appropriately. When you round, you focus on adjusting the number to the closest significant figure based on its place value.

Nearest Hundred

When rounding to the nearest hundred, you need to look at the number in the tens place to determine whether to round up or down. For instance, in the number 199:

• The tens digit is '9', which is more than 5. So, we round up.
• Hence, 199 gets rounded up to 200 since it's closer to 200 than to 100.

The rule of thumb is that if the digit in tens is 5 or more, round up. If it's less than 5, round down. This concept helps simplify numbers, making them more manageable and easier to work with.

Nearest Thousand

Rounding to the nearest thousand means assessing whether the number is closer to the current thousand or the next. For 199, notice the following:

• The number is far below 500, which means it’s closer to 0 than 1000.
• Therefore, 199 rounded to the nearest thousand becomes 0.

This step ensures clarity and simplification when handling numbers in calculations. As numbers get smaller compared to the place value, they tend to round down to zero.

Nearest Million

The nearest million requires examining if a number is closer to 0 or moving towards the million mark. Take 199 as an example:

• Since 199 is nowhere near 500,000 or 1,000,000, it rounds down to zero.

Understanding this step allows for working with large figures efficiently by clearing out smaller values that have minimal impact when considering multiples of a million. It's crucial for estimations in large scale computations or data handling.