Solved Exercises on Writing Numbers in Standard Form in Grade 4

Master writing numbers in standard form: converting from word form, expanded form, and place value understanding through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Word form to standard form
Exercise 1
Write "four hundred twenty-seven thousand, five hundred eighty-three" in standard form.
Definition:

Standard form: Writing a number using digits and commas to separate periods. Word form: Writing a number using words instead of digits.

Word to standard form method:
  1. Identify the periods mentioned in the words
  2. Write the digits for each period
  3. Use commas to separate periods
  4. Fill in zeros for missing places
  5. Verify the number matches the word form
Word form
Four hundred twenty-seven thousand, five hundred eighty-three
Thousands period
427
Ones period
583
Standard form
427,583
Step 1: Identify the periods

"four hundred twenty-seven thousand" and "five hundred eighty-three"

Step 2: Write the thousands period

"four hundred twenty-seven" = 427

Step 3: Write the ones period

"five hundred eighty-three" = 583

Step 4: Combine with comma

427,583

Step 5: Verify the conversion

427,583 = four hundred twenty-seven thousand, five hundred eighty-three ✓

427,583
Final answer:

The standard form is 427,583

Applied rules:

• Period identification: Recognize thousands and ones periods

• Comma placement: Place comma after thousands period

• Verification: Check that the standard form matches the word form

2 Expanded form to standard form
Exercise 2
Write the number represented by 300,000 + 50,000 + 7,000 + 400 + 20 + 8 in standard form.
Definition:

Expanded form: Writing a number as the sum of the values of each digit. To convert to standard form, add all the parts together.

Expanded form
300,000 + 50,000 + 7,000 + 400 + 20 + 8
Addition
357,428
Step 1: Identify each part of the expanded form

300,000 + 50,000 + 7,000 + 400 + 20 + 8

Step 2: Add the values together

300,000 + 50,000 = 350,000

350,000 + 7,000 = 357,000

357,000 + 400 = 357,400

357,400 + 20 = 357,420

357,420 + 8 = 357,428

Step 3: Verify by converting back to expanded form

357,428 = 300,000 + 50,000 + 7,000 + 400 + 20 + 8 ✓

Step 4: State the answer

The standard form is 357,428

357,428
Final answer:

The standard form is 357,428

Applied rules:

• Addition: Sum all the expanded parts

• Place value: Each digit maintains its place value

• Verification: Check by converting back to expanded form

3 Place value to standard form
Exercise 3
Write the number that has 6 in the hundred thousands place, 4 in the ten thousands place, 2 in the thousands place, 8 in the hundreds place, 1 in the tens place, and 7 in the ones place.
Definition:

Place value: The value of a digit based on its position in a number. Each position represents a power of 10.

Hundred thousands
6
Ten thousands
4
Thousands
2
Hundreds
8
Tens
1
Ones
7
Step 1: Write the place value chart

Hundred thousands, Ten thousands, Thousands, Hundreds, Tens, Ones

Step 2: Fill in each place with the given digit

6 in hundred thousands: 600,000

4 in ten thousands: 40,000

2 in thousands: 2,000

8 in hundreds: 800

1 in tens: 10

7 in ones: 7

Step 3: Combine the digits

642,817

Step 4: Verify each place value

642,817: 6 in hundred thousands, 4 in ten thousands, 2 in thousands, 8 in hundreds, 1 in tens, 7 in ones ✓

642,817
Final answer:

The standard form is 642,817

Applied rules:

• Place order: Arrange from highest to lowest place value

• Digit placement: Each digit goes in its designated place

• Verification: Check that each digit is in the correct place

Rules and methods, laws,...
Standard Form = Digits + Commas
Standard Form
Number Forms
Word Form
Four hundred twenty-seven thousand
Number Forms
Standard Form
427,000
Number Forms
Expanded Form
400,000 + 20,000 + 7,000
Key definitions:

Standard form: Writing a number using digits and commas to separate periods (e.g., 427,583).

Word form: Writing a number using words instead of digits (e.g., four hundred twenty-seven thousand, five hundred eighty-three).

Expanded form: Writing a number as the sum of the values of each digit (e.g., 400,000 + 20,000 + 7,000 + 500 + 80 + 3).

Period: A group of three digits in a number, separated by commas (ones, thousands, millions).

Place value: The value of a digit based on its position in a number.

Comma placement: Commas are placed every three digits from right to left to separate periods.

Standard form conversion methodology:
  1. Identify the form: Determine if you're converting from word form, expanded form, or place value
  2. Extract digits: Identify each digit and its corresponding place value
  3. Arrange digits: Place digits in order from highest to lowest place value
  4. Add commas: Insert commas every three digits from right to left
  5. Verify: Check that your standard form matches the original representation
Tip 1: Remember that commas separate periods: thousands, millions, etc.
Tip 2: When converting from word form, look for "thousand," "million" to identify periods.
Tip 3: When converting from expanded form, add all parts together.
Tip 4: Practice with place value charts to visualize the positions.
Common errors: Forgetting commas, misplacing commas, not filling in zeros for missing places, confusing place values, reading numbers incorrectly.
Real-world applications: Reading population counts, distances, money amounts, scores, measurements, statistics, and any large numbers encountered in daily life.
Standard form rules:

• Comma placement: Every three digits from right to left

• Period names: Ones, Thousands, Millions

• Leading zeros: Not written in standard form

• Zero handling: Include zeros in middle positions

• Verification: Convert back to original form to check accuracy

Solution: Exercises 4 to 5
4 Mixed conversion
Exercise 4
A city has a population of "eight hundred forty-three thousand, two hundred fifty-six" people. Write this number in standard form.
Definition:

Mixed conversion: Problems that involve converting from word form to standard form, often embedded in real-world contexts.

Word form
Eight hundred forty-three thousand, two hundred fifty-six
Thousands period
843
Ones period
256
Standard form
843,256
Step 1: Identify the periods in the word form

"eight hundred forty-three thousand" and "two hundred fifty-six"

Step 2: Convert the thousands period

"eight hundred forty-three" = 843

Step 3: Convert the ones period

"two hundred fifty-six" = 256

Step 4: Combine with comma

843,256

Step 5: Verify the conversion

843,256 = eight hundred forty-three thousand, two hundred fifty-six ✓

843,256
Final answer:

The population is 843,256 people.

Applied rules:

• Period identification: Recognize thousands and ones periods

• Context: Apply conversion in real-world scenario

• Verification: Check that the standard form matches the word form

5 Problem-solving with standard form
Exercise 5
Write the number that has 2 in the hundred thousands place, 0 in the ten thousands place, 5 in the thousands place, 0 in the hundreds place, 3 in the tens place, and 7 in the ones place.
Definition:

Zero handling: When writing numbers in standard form, zeros in middle positions must be included to maintain the correct place value.

Hundred thousands
2
Ten thousands
0
Thousands
5
Hundreds
0
Tens
3
Ones
7
Step 1: Identify each place value

Hundred thousands: 2, Ten thousands: 0, Thousands: 5, Hundreds: 0, Tens: 3, Ones: 7

Step 2: Write each digit in its place

205,037

Step 3: Notice the zeros

Zeros in ten thousands and hundreds places are crucial for correct value

Step 4: Verify the number

205,037: 2 in hundred thousands, 0 in ten thousands, 5 in thousands, 0 in hundreds, 3 in tens, 7 in ones ✓

Step 5: State the answer

The standard form is 205,037

205,037
Final answer:

The standard form is 205,037

Applied rules:

• Zero inclusion: Zeros in middle positions must be written

• Place maintenance: Each digit maintains its place value

• Verification: Check that each digit is in the correct place

Complete Summary: Writing Numbers in Standard Form
Standard Form = Digits + Commas
Standard Form
Key definitions:

Standard form: Writing a number using digits and commas to separate periods. This is the most common way we write numbers (e.g., 427,583).

Word form: Writing a number using words instead of digits (e.g., four hundred twenty-seven thousand, five hundred eighty-three).

Expanded form: Writing a number as the sum of the values of each digit (e.g., 400,000 + 20,000 + 7,000 + 500 + 80 + 3).

Period: A group of three digits in a number, separated by commas (ones, thousands, millions).

Place value: The value of a digit based on its position in a number (ones, tens, hundreds, thousands, ten thousands, hundred thousands).

Comma placement: Commas are placed every three digits from right to left to separate periods.

Zero handling: Zeros in middle positions must be included to maintain correct place value.

Complete standard form conversion methodology:
  1. Identify the form: Determine if you're converting from word form, expanded form, or place value
  2. Extract digits: Identify each digit and its corresponding place value
  3. Arrange digits: Place digits in order from highest to lowest place value
  4. Include zeros: Write zeros for any missing place values
  5. Add commas: Insert commas every three digits from right to left
  6. Verify: Check that your standard form matches the original representation
Tip 1: Remember that commas separate periods: thousands, millions, etc.
Tip 2: When converting from word form, look for "thousand," "million" to identify periods.
Tip 3: When converting from expanded form, add all parts together.
Tip 4: Never omit zeros in middle positions - they maintain place value!
Tip 5: Practice with place value charts to visualize the positions.
Common errors: Forgetting commas, misplacing commas, not filling in zeros for missing places, confusing place values, reading numbers incorrectly, omitting zeros in middle positions.
Real-world applications: Reading population counts, distances, money amounts, scores, measurements, statistics, scientific data, and any large numbers encountered in daily life.
Standard form principles:

• Comma placement: Every three digits from right to left

• Period names: Ones, Thousands, Millions

• Leading zeros: Not written in standard form

• Zero handling: Include zeros in middle positions to maintain place value

• Verification: Convert back to original form to check accuracy

• Place order: Arrange from highest to lowest place value

• Digit placement: Each digit goes in its designated place

Visual Guide to Writing Numbers in Standard Form

🔢
Place Value Chart

Hundred Thousands: 100,000

Ten Thousands: 10,000

Thousands: 1,000

Hundreds: 100

Tens: 10

Ones: 1

Example: 473,829

Word to Standard Form

Identify periods: "thousand," "million"

Write each period separately

Combine with commas

Example: Four hundred twenty-seven thousand = 427,000

Expanded to Standard Form

Add all parts together

Each digit maintains place value

Example: 300,000 + 50,000 + 7,000 = 357,000

Zero Handling

Never omit zeros in middle positions

Zeros maintain correct place value

Example: 205,037 (not 25,37)

Questions & Answers

Question: I sometimes forget where to put commas when writing numbers in standard form. How can I remember?

Answer: Here's a helpful way to remember comma placement:

  • Count from the right: Start at the ones place and count 3 digits to the left
  • Place commas: Put a comma after every 3rd digit from the right
  • Remember periods: Each group of 3 digits is called a period

Example: For 427583, count from right: 583 (ones period), then 427 (thousands period). So it's 427,583.

Practice by counting backwards from the right: ones, tens, hundreds (comma), thousands, ten thousands, hundred thousands (comma), millions.

The commas separate thousands, millions, billions, etc.

Question: When converting from word form, I get confused about which words go in which period. How do I know?

Answer: Look for key words that indicate periods:

  • "Thousand" separates periods: Everything before "thousand" is the thousands period
  • "Million" separates periods: Everything before "million" is the millions period
  • Words after "thousand" but before comma: These are the ones period

Example: "four hundred twenty-seven thousand, five hundred eighty-three"

- "four hundred twenty-seven" comes before "thousand" → 427 in thousands period

- "five hundred eighty-three" comes after "thousand" → 583 in ones period

So it's 427,583.

The comma after "thousand" separates the periods!

Question: What if there's a zero in the word form? Do I still write it in the standard form?

Answer: Yes, you must include zeros in the standard form! Zeros are crucial for maintaining place value:

  • Leading zeros: Not written at the beginning (00427 = 427)
  • Middle zeros: Must be written to maintain place value
  • Trailing zeros: Written at the end after other digits

Example: "two hundred five thousand, thirty-seven" = 205,037

Notice the zeros in the ten thousands place and hundreds place - these are essential!

If you wrote 25,37 instead of 205,037, the number would be much smaller and incorrect.

Zeros in middle positions maintain the correct value of each digit!