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Chapter 1: Problem 59

Write the number in standard form. five hundred two thousand one hundred forty

Short Answer

Expert verified
The number 'five hundred two thousand one hundred forty' written in standard form is 502,140.

Step by step solution

01

Identify the Hundreds Place

The number 'five hundred' represents the hundreds place and equals 500. In the standard numerical form, this would be written as 500.
02

Identify the Thousands Place

The phrase 'two thousand' indicates the thousands place, which equates to 2000. In standard numerical form, this would be put as 2000.
03

Identify the Remaining Digits

Lastly, the phrase 'one hundred forty' represents the remaining digits, translating to 140 in standard numerical form.
04

Combine all Parts

To get the final answer, add all of the identified values together. In this case, combine '500','2000' and '140'. So, '500' + '2000' + '140' equals '502,140'.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Place Value
Understanding place value is crucial when writing numbers in standard form, especially with larger numbers. Each digit in a number has a specific position, which we call its "place value." This tells us how much the digit contributes to the overall number.
For example, in the number 502,140, each digit is in a different place value:
  • The digit '5' is in the hundreds of thousands place, indicating 500,000.
  • The digit '0' follows, in the ten thousands place, so it adds no additional value.
  • '2' is in the thousands place, which adds 2,000.
  • The '1' comes next in the hundreds place, contributing 100.
  • The '4' sits in the tens place, adding 40.
  • Finally, '0' in the ones place adds nothing more.
Breaking down a number based on its place value helps recognize and understand its full value. This knowledge allows you to correctly form and understand numbers that are expressed using words.
Numerical Form
Numerical form is the way of representing numbers using digits, as opposed to words or other representations. In our example, the words 'five hundred two thousand one hundred forty' can be translated into the numerical form as 502,140.
To convert from words to numerical form, follow these steps:
  • Write each component: Start with larger place values, such as thousands or millions, and then move to smaller place values. For instance, 'two thousand' becomes 2000.
  • List each number separately: Write out each separate number found within the text. 'Five hundred' is written as 500.
  • Identify smaller units: Lastly, convert smaller units like 'one hundred forty' to 140.
Once written, combine all the numerical forms to find the entire number. Ensure all numbers are placed correctly according to place value, resulting in an accurate representation like 502,140 in this case.
Addition
Addition is a fundamental math operation used to find the total of two or more numbers. It is crucial when combining numbers that have been broken into parts, such as when converting a written number into standard form.
To add numbers, align the numbers by their rightmost digits (the ones place) before adding each column starting from the right:
  • Thousands: Add the thousands together: 2000 + (other thousands if any).
  • Hundreds: Add the hundreds: 500 (plus any other hundreds).
  • Remaining Places: Finally, add any additional numbers like 140, ensuring alignment in their correct place values.
For our example, adding 2000 (thousands place) + 500 (hundreds) + 140 (tens and units) results in the total 502,140.
Using addition to combine each component helps form the standard numerical representation from its separate words.

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