Problem 462 - Prealgebra

Question

Name each number in words. $$204,614$$

Step-by-Step Solution

Answer

Two hundred four thousand, six hundred fourteen.

Step 1: Understanding the Place Values

Split the number into its component place values: 204,614 has digits in the hundred-thousands, ten-thousands, thousands, hundreds, tens, and ones places.

Step 2: Analyze the Hundred-Thousands and Ten-Thousands Places

204 is in the hundred-thousands place, so it is two hundred four thousand.

Step 3: Analyze the Thousands Place

Since there is no digit immediately in the thousands place in '204,000', it's simply 'thousand'.

Step 4: Analyze the Hundreds Place

Move to the hundreds place which is 6, so it is 'six hundred'.

Step 5: Analyze the Tens and Ones Places

The '14' combines the ten and one places to form 'fourteen'.

Step 6: Combine All Parts Together

Putting it all together, 204,614 is 'two hundred four thousand, six hundred fourteen'.

Key Concepts

Place Value

Understanding place value is the foundation of reading and writing large numbers. Every digit in a number has a specific place, or position, that determines its value. For instance, in the number 204,614, each digit is part of a 'place':

• 2 is in the hundred-thousands place.
• 0 is in the ten-thousands place.
• 4 is in the thousands place.
• 6 is in the hundreds place.
• 1 is in the tens place.
• 4 is in the ones place.

Each of these places is weighted differently, meaning that a digit's value depends on its place. For example, the 2 in 204,614 is not just 2; it is actually 200,000 because it's in the hundred-thousands place. Knowing this helps in breaking down and understanding large numbers more efficiently.

Reading Large Numbers

Reading large numbers can initially seem daunting, but with the right approach, it becomes straightforward. Start by breaking the number into more manageable chunks. When you see 204,614, split it into 204 and 614. This breaks down into:

• **204: ** This part reads 'two hundred four thousand.' This tells us the quantity of thousands in the number.
• **614: ** This section covers the lower place values: 'six hundred fourteen.'

When reading large numbers, it's important to state each place value correctly and put emphasis on larger units first, followed by smaller units. Take your time, and read each segment out loud. This method helps ensure that no digit or place value is overlooked.

Writing Numbers in Words

Writing numbers in words either solidifies your understanding or helps communicate exact quantities clearly. Follow these steps to get it right every time:

• Break It Down: Segment the number by its place values. For 204,614, separate it into 204 and 614.
• Start from the Left: Begin with the highest place value. For 204, write 'two hundred four' and remember to add 'thousand'. So you get 'two hundred four thousand.'
• Add the Next Segment: Move to the next group of numbers, 614. Write it out as 'six hundred fourteen.'
• Combine Everything: Put all segments together to write the full number in words. 204,614 becomes 'two hundred four thousand, six hundred fourteen.'

Following these steps ensures that you accurately write large numbers in words, making it easier to read and understand them in textual form.