Problem 15 - Fundamentals of Mathematics

Question

For the following problems, write all numbers in words. $$201,040$$

Step-by-Step Solution

Answer

Two hundred one thousand forty.

Step 1: Identify the Place Values

First, understand the place values of the given number: \( 201,040 \). From left to right, the digits are in the hundred thousands, ten thousands, thousands, hundreds, tens, and ones places.

Step 2: Break Down the Number

Separate the given number \( 201,040 \) into its important components based on the place values. This would be 200,000 (two hundred thousand), 1,000 (one thousand), and 40 (forty).

Step 3: Write Each Component in Words

Convert each section that we identified: 200,000 becomes 'two hundred thousand', 1,000 becomes 'one thousand', and 40 becomes 'forty'.

Step 4: Combine the Words

Combine all the parts we've converted into words to form the final sentence: 'Two hundred one thousand forty.'

Key Concepts

Writing Numbers in Words

Writing numbers in words is the process of expressing numbers as text. This helps in improving your understanding of the number itself and ensures clarity in communication, especially where precise numbers are essential.

• The first step in writing numbers in words involves identifying the place values of individual digits.
• Next, you break down the number into segments that are easier to manage.
• Finally, you write these segments in textual form and combine them to express the full number in words.

For example, converting the number 201,040 starts with recognizing the various segments, such as two hundred thousand, one thousand, and forty, eventually forming 'Two hundred one thousand forty' when combined.

Hundreds Place

The hundreds place in a number is the third digit from the right in a standard form numerical representation. It indicates how many hundreds are in a number.

• Every digit in the hundreds place is multiplied by 100.
• It's essential for understanding the magnitude of a number by contributing significantly to its overall value.

For the number 201,040, the hundreds place is represented by the digit '0', which implies there are zero hundreds contributing to the number. This keeps the hundreds value at bay and adds simplicity to our calculations for this specific number.

Thousands Place

The thousands place is crucial in understanding numbers beyond simple hundreds and thousands. It is the fourth digit from the right.

• This place represents groups of one thousand, showing how many thousand are in the number.
• Finding this place involves counting four positions from the rightmost digit in a number.

In 201,040, the digit '1' occupies the thousands place, signifying that there is precisely one set of one thousand. This becomes the key factor in correctly stating and writing the number in words as part of the overall number composition.

Number Decomposition

Number decomposition is breaking down a large number into smaller, comprehensible parts. It's like turning a big puzzle into smaller, manageable pieces.

• This process helps in grasping and simplifying complex numbers.
• It involves separating a number based on its place values.

With 201,040, decomposition means identifying separately: 200,000 (two hundred thousand), 1,000 (one thousand), and 40 (forty). By doing this, we manage to strategically break down the number for easier interpretation and presentation.