Problem 13 - Prealgebra

Question

In the following exercises, name each number in words. $$1,078$$

Step-by-Step Solution

Answer

One thousand seventy-eight

Step 1: Identify the Components

Determine the place value of each digit in the number. For 1,078, the digit positions are: 1 (thousands), 0 (hundreds), 7 (tens), and 8 (ones).

Step 2: Convert Each Digit to Words

Convert each digit in its place value to words. The digit '1' in the thousands place becomes 'one thousand'. The digit '0' in the hundreds place is not spoken. The digit '7' in the tens place becomes 'seventy'. The digit '8' in the ones place becomes 'eight'.

Step 3: Combine the Words

Combine the words for each place value, skipping zeroes. 'One thousand seventy-eight' is the combination of the thousands, tens, and ones places.

Key Concepts

Understanding Place Value

Place value is an essential concept in mathematics. It helps us understand the value of each digit in a number based on its position. For the number 1,078, let's break it down by its place values as per the step-by-step solution.
Each digit has a place value:

• The digit 1 is in the thousands place, so its value is 1,000.
• The digit 0 is in the hundreds place, but it doesn't contribute any value.
• The digit 7 is in the tens place, so its value is 70.
• The digit 8 is in the ones place, so its value is 8.

Understanding place value helps us when we need to convert numbers to words or perform other operations with numbers. It's the foundation for everything in arithmetic.

Digit Conversion to Words

Next, let's convert each digit in our number to words.
Starting with the thousands place: the digit 1 is converted to 'one thousand'. Notice how we mention the place value after the digit. For the hundreds place, we have a 0, which is not spoken out.
Then, we move to the tens place: the digit 7 is converted to 'seventy'. Finally, in the ones place: the digit 8 is converted to 'eight'.
Here’s a quick guide to remember:

• Thousands place: 'n thousand'
• Hundreds place: 'n hundred' (if the digit is not zero)
• Tens place: use 'ten', 'twenty', 'thirty', etc.
• Ones place: simple digit names ('one', 'two', 'three', etc.)

By converting each digit, you break down the number, making it easier to express in words.

Combining Number Words

Finally, let’s combine the words from the previous step.
Start with the highest place value and work down to the lowest, skipping zeroes.
For 1,078, we have:

• 'one thousand' from the thousands place
• Nothing from the hundreds place, since it's zero
• 'seventy' from the tens place
• 'eight' from the ones place

When you put it all together, you get 'one thousand seventy-eight'.
This step-by-step approach makes it simple to convert and combine number words accurately. You now have the knowledge to tackle different numbers and express them clearly with confidence!