Problem 581 - Prealgebra

Question

Write each number as a whole number using digits. (a) six hundred thirteen (b) fifty-five thousand two hundred eight

Step-by-Step Solution

Answer

(a) 613, (b) 55,208

Step 1: Understanding Whole Numbers

Whole numbers are non-negative numbers without any fractional or decimal parts. They include 0, 1, 2, 3, etc. To convert a word form of a number to its digit form, identify each place value.

Step 2: Identify Hundreds in Part (a)

In part (a), 'six hundred thirteen,' the term 'six hundred' represents 600.

Step 3: Identify Tens and Units in Part (a)

In part (a), 'thirteen' is made up of 10 plus 3, or simply 13. Combining this with the previous step gives the number 613.

Step 4: Combine to Form Whole Number in Part (a)

Combine the values identified: 600 (hundreds) + 13 (units) = 613. Therefore, 'six hundred thirteen' is written as 613.

Step 5: Identify Thousands in Part (b)

In part (b), 'fifty-five thousand' represents 55,000.

Step 6: Identify Hundreds, Tens, and Units in Part (b)

In part (b), 'two hundred eight' represents 208.

Step 7: Combine to Form Whole Number in Part (b)

Combine the values identified: 55,000 (thousands) + 208 (units) = 55,208. Therefore, 'fifty-five thousand two hundred eight' is written as 55,208.

Key Concepts

Place Value

Understanding place value is crucial when working with whole numbers. Each digit in a number has a specific place value that denotes its position. The place values increase by powers of ten from right to left. Here's a quick breakdown:

• Units place (1s)
• Tens place (10s)
• Hundreds place (100s)
• Thousands place (1,000s)

To convert a number from word form to digit form, we need to identify the place value of each component from the word description. For example, in the number 'six hundred thirteen,' the 'six hundred' part signifies the hundreds place, and 'thirteen' signifies the combination of tens and units.Understanding place value simplifies converting long and complex number phrases into their digit representations.

Number Conversion

Converting numbers from word form to digit form involves several steps. These steps help break down the word descriptions into manageable parts:1. **Identify larger place values:** Start by understanding the largest place value in the word form. For example, in 'fifty-five thousand two hundred eight,' first identify 'fifty-five thousand' as 55,000.2. **Identify smaller place values:** Next, break down the remaining parts. For 'two hundred eight,' represent it as 200 + 8 = 208.3. **Combine all parts:** Add the identified parts together to get the final whole number. From our earlier example, combining 55,000 and 208 results in 55,208.This method ensures that you account for all place values accurately and form the correct whole number.

Digit Representation

Digit representation deals with writing numbers using digits instead of words. Each digit is placed according to its place value to form the whole number.For part (a) of the exercise, 'six hundred thirteen,' we:

• Identify 'six hundred' as 600.
• Recognize 'thirteen' as 13 (10 + 3).
• Combine these: 600 + 13 = 613.

For part (b), 'fifty-five thousand two hundred eight,' we:

• Identify 'fifty-five thousand' as 55,000.
• Recognize 'two hundred eight' as 208 (200 + 8).
• Combine these: 55,000 + 208 = 55,208.

This process translates the word description of a number into its precise digit representation, making it easier to understand and use in mathematical operations.