Problem 30 - Prealgebra

Question

In the following exercises, name each number in words. The population of India is estimated at 1,267,401,849 as of July 1, 2014.

Step-by-Step Solution

Answer

One billion, two hundred sixty-seven million, four hundred one thousand, eight hundred forty-nine.

Step 1: Identify the Number

Look at the provided number carefully: 1,267,401,849.

Step 2: Break down the Number

Break the number into groups of three digits from right to left. For example, 1,267,401,849 can be broken down as 1 (billion), 267 (million), 401 (thousand), and 849 (hundred).

Step 3: Name Each Group

Convert each group into words. 1 is 'One', 267 is 'Two Hundred Sixty-Seven', 401 is 'Four Hundred One', 849 is 'Eight Hundred Forty-Nine'.

Step 4: Combine the Groups

Combine the words with the appropriate place value designations: 'One Billion', 'Two Hundred Sixty-Seven Million', 'Four Hundred One Thousand', 'Eight Hundred Forty-Nine'.

Step 5: Write the Full Name

Combine all the named groups into a full sentence: 'One billion, two hundred sixty-seven million, four hundred one thousand, eight hundred forty-nine'.

Key Concepts

Understanding Place Value

Place value is a fundamental concept in understanding numbers. It refers to the value of a digit based on its position in a number. For example, in the number 1,267,401,849, the digit 1 in the billion place represents one billion, while the digit 1 in the hundred place represents one hundred. This is because the place of each digit (ones, tens, hundreds, thousands, etc.) determines its value.

Here's a breakdown:

• Units: 9
• Tens: 40
• Hundreds: 800
• Thousands: 1,000
• Ten thousands: 60,000
• Hundred thousands: 700,000
• Millions: 2,000,000
• Ten Millions: 60,000,000
• Hundred Millions: 200,000,000
• Billions: 1,000,000,000

By understanding place value, you can better grasp the size and scale of numbers, which makes reading and interpreting them easier.

Grouping Large Numbers

To make large numbers more manageable, they are often broken into groups of three digits, starting from the right. These groups are known as periods, and each group is typically separated by commas or spaces.

For example, the number 1,267,401,849 is divided into the following groups:

• 1 (billion)
• 267 (million)
• 401 (thousand)
• 849 (hundred)

Grouping makes it easier to read and write large numbers.

Read each period separately and combine them with the appropriate place value descriptions (i.e., billion, million, thousand, hundred).
This systematic approach allows us to accurately read, write, and understand large numbers.

Writing Number Names

Writing number names involves converting each group of digits into words and then combining them with their place value descriptions.

Taking the number 1,267,401,849 as an example:

• First, break it down as 1 (billion), 267 (million), 401 (thousand), and 849 (hundred).
• Then, convert each group into words:
• 1 becomes 'one'.
• 267 becomes 'two hundred sixty-seven'.
• 401 becomes 'four hundred one'.
• 849 becomes 'eight hundred forty-nine'.

Finally, combine these with their place values:
'One billion, two hundred sixty-seven million, four hundred one thousand, eight hundred forty-nine.'

Ensuring each group is properly named and combined with its place value makes reading and writing large numbers less daunting.