Problem 17 - Fundamentals of Mathematics

Question

For the following problems, write all numbers in words. $$16,000,053$$

Step-by-Step Solution

Answer

Sixteen million fifty-three.

Step 1: Break Down the Number

The given number is 16,000,053. First, identify the components of the number by grouping the digits according to their position. This helps in understanding the number in terms of units, thousands, and millions.

Step 2: Write the Million Place

The number has '16' in the millions place. Therefore, write 'sixteen million' to cover the million category.

Step 3: Consider the Thousand Place

After '16 million', we have '000', which represents zero in the thousand place. This means we can skip writing anything related to thousands, keeping the number in words concise.

Step 4: Look at the Units Place

Finally, consider the last three digits, '053', which corresponds to fifty-three in the units place. Write 'fifty-three' for these last digits.

Step 5: Combine All Parts

Combine the number words from each category. The number 16,000,053 in words becomes 'sixteen million fifty-three' as there is no need to include the word for zero thousands.

Key Concepts

Understanding Place Value

Place value is a key concept in understanding large numbers. It refers to the value of each digit in a number depending on its position. For instance, in the number 16,000,053, each digit has a specific place value based on whether it is in the units, thousands, or millions group. This system makes it easier to read and write big numbers without confusion.

• The rightmost digit is the units place.
• The next digit to the left is the tens place, followed by hundreds, thousands, tens of thousands, and so on.

By understanding place value, you can break down a number like 16,000,053 into smaller, more manageable parts. In this way, recognizing and recording each place value helps you to pinpoint the digits that are significant and require naming when writing numbers in words.

Writing Numbers in Words

To write numbers in words, start by breaking down the number based on its place values. This process involves identifying each segment of the number, such as millions, thousands, and units, and converting them into words. When dealing with a number like 16,000,053, handle each part systematically to ensure accuracy.

• First, look at the millions place. Here we have the number '16', which we write as 'sixteen million.'
• Next, observe the thousands and units portions of the number. If there are zero thousands as in this case, you can skip them for simplicity.
• Finally, focus on the units part, '053.' Convert this to 'fifty-three.'

This method ensures you cover all parts of the number without leaving anything important out. By combining these carefully translated segments, you effectively write 16,000,053 as 'sixteen million fifty-three,' keeping your expression clear and precise.

Steps of Mathematics Instruction

Mathematics instruction often involves clear steps to break down and solve a problem, similar to the process used in converting numbers to words. By following a structured approach, students can improve their understanding of mathematical concepts and practices.
Following steps like those outlined in the solution for writing numbers ensures a logical progression that’s easy to follow. Here’s a simplified structure:

• **Identify the problem:** Clearly understand what is being asked. In the number context, read the entire number.
• **Break it down:** Divide the problem into smaller parts, such as place values in a number.
• **Translate and combine:** Convert each part into words or a solution, and then combine them.

This method helps students develop strong problem-solving skills and lays a solid foundation for tackling more complex mathematical challenges. By applying such a structured approach, learning becomes less daunting and more achievable.