Problem 18 - Prealgebra

Question

In the following exercises, name each number in words. $$1,458,398$$

Step-by-Step Solution

Answer

One million, four hundred fifty-eight thousand, three hundred ninety-eight.

Step 1: Identify the Number

The number given in the exercise is 1,458,398.

Step 2: Break Down the Number

First, separate the number into groups of three digits from right to left. This will make it easier to read. Hence, 1,458,398 becomes 1,458, and 398.

Step 3: Name Each Group in Words

Read each group of digits as if it were a single number. The first group, 1,458, is read as 'one million, four hundred fifty-eight thousand'. The second group, 398, is read as 'three hundred ninety-eight'.

Step 4: Combine the Words

Combine the words for each group to name the entire number. The combined phrase is 'one million, four hundred fifty-eight thousand, three hundred ninety-eight'.

Key Concepts

Reading Large Numbers

Reading large numbers can seem tricky at first, but with some practice, you'll find it becomes much easier! To read large numbers, it's important to break them down into smaller groups.
Start by dividing the number into groups of three digits, starting from the right. These groups are called periods. Each period has its own name (thousands, millions, billions, etc.) which helps in reading the entire number.
For example, if you have the number 1,458,398, the first step is to split it into groups: 1,458 and 398. By reading each group separately, and then combining them, you can accurately name the number in words.
This practice makes it easy to understand and read large numbers comfortably!

Place Value

Understanding place value is key to reading and writing large numbers. Each digit in a number has a specific place value, depending on its position.
Let's take the number 1,458,398. Each digit from right to left has a value of ones, tens, hundreds, thousands, ten thousands, hundred thousands, and millions.
For instance:

• The digit 8 is in the ones place.
• The digit 9 is in the tens place.
• The digit 3 is in the hundreds place.
• Moving to the left three more places, the digit 8 is in the ten thousands place.
• The digit 5 is in the hundred thousands place.
• And the digit 4 is in the millions place.

Understanding these place values helps you break down and read large numbers effectively.

Number Grouping

Number grouping simplifies the process of reading and writing large numbers by dividing the digits into smaller, more manageable parts.
When we group numbers, typically we do so in sets of three digits, called 'periods.' These periods make it easier to see place values and read the numbers fluently.
Take the number 1,458,398. It can be split into two groups: 1,458 and 398. The first set (1,458) is the thousands period, and the second set (398) is the units period.
When you read the number, you handle each group as a smaller number. So, 'one million, four hundred fifty-eight thousand' and 'three hundred ninety-eight' gives 'one million, four hundred fifty-eight thousand, three hundred ninety-eight'.
This grouping method universally aids in reading and writing even larger numbers with accuracy and ease.