Solved Exercises on Reading Numbers Up to 1,000,000 in Grade 4

Master reading numbers up to 1,000,000: place value, number names, expanded form, comparing large numbers, and problem-solving strategies through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Place value identification
Exercise 1
What is the value of the digit 7 in the number 473,829? What place does it occupy?
Definition:

Place value: The value of a digit based on its position in a number. Each position represents a power of 10. The positions from right to left are: Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Millions.

Place value method:
  1. Identify the position of the digit from right to left
  2. Count the positions starting from 0 (ones place)
  3. Determine the place name based on the position
  4. Calculate the value by multiplying the digit by its place value
Number
473,829
Digit
7
Position
Ten Thousands
Step 1: Write the number with commas

473,829

Step 2: Count positions from right to left

9(ones), 2(tens), 8(hundreds), 3(thousands), 7(ten thousands), 4(hundred thousands)

Step 3: Identify the digit's position

The digit 7 is in the fifth position from the right

Step 4: Name the place

The fifth position from the right is the ten thousands place

Step 5: Calculate the value

7 × 10,000 = 70,000

Value: 70,000, Place: Ten Thousands
Final answer:

The digit 7 is in the ten thousands place and has a value of 70,000.

Applied rules:

• Position counting: Count from right to left starting at position 0

• Place names: Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands

• Value calculation: Digit × Place value

2 Number names
Exercise 2
Write the number 642,817 in words.
Definition:

Number names: Writing numbers using words instead of digits. For numbers up to 1,000,000, separate the hundreds, tens, and ones in each period (thousands and ones) and use hyphens for compound numbers like twenty-one.

Number
642,817
Periods
642 thousands and 817 ones
In words
Six hundred forty-two thousand eight hundred seventeen
Step 1: Separate the periods

642,817 has two periods: 642 (thousands) and 817 (ones)

Step 2: Write the thousands period

642 = six hundred forty-two

Step 3: Add the word "thousand"

six hundred forty-two thousand

Step 4: Write the ones period

817 = eight hundred seventeen

Step 5: Combine both periods

six hundred forty-two thousand eight hundred seventeen

Step 6: Check compound numbers

Forty-two and seventeen are correctly hyphenated

Six hundred forty-two thousand eight hundred seventeen
Final answer:

Six hundred forty-two thousand eight hundred seventeen

Applied rules:

• Period separation: Separate thousands from ones with comma

• Hyphenation: Use hyphens for compound numbers from 21-99

• Word order: Write thousands period first, then ones period

3 Expanded form
Exercise 3
Write 357,428 in expanded form.
Definition:

Expanded form: Writing a number as the sum of the values of each digit. Each digit is multiplied by its place value.

Number
357,428
Expanded
300,000 + 50,000 + 7,000 + 400 + 20 + 8
Step 1: Identify each digit and its place value

3 (hundred thousands), 5 (ten thousands), 7 (thousands), 4 (hundreds), 2 (tens), 8 (ones)

Step 2: Write each digit's value

3 × 100,000 = 300,000

5 × 10,000 = 50,000

7 × 1,000 = 7,000

4 × 100 = 400

2 × 10 = 20

8 × 1 = 8

Step 3: Add all the values together

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

Step 4: Verify the expanded form

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

300,000 + 50,000 + 7,000 + 400 + 20 + 8
Final answer:

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

Applied rules:

• Digit value: Each digit multiplied by its place value

• Sum of parts: All expanded parts should add up to the original number

• Place value: Correctly identify the value of each position

Rules and methods, laws,...
Digit × Place Value = Digit's Value
Place Value
Place Values
Hundred Thousands
100,000
Place Values
Ten Thousands
10,000
Place Values
Thousands
1,000
Key definitions:

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

Period: A group of three digits in a number separated by commas. The main periods are ones, thousands, millions.

Expanded form: Writing a number as the sum of the values of each digit.

Standard form: Writing a number using digits.

Word form: Writing a number using words.

Comma placement: Commas separate periods in numbers, placed every three digits from right to left.

Number reading methodology:
  1. Identify periods: Separate the number into groups of three digits
  2. Determine place values: Know the value of each position
  3. Read each period: Read the digits in each period as if they were in the ones period
  4. Add period names: Include "thousand" for the thousands period
  5. Combine periods: Read the entire number as a whole
Tip 1: Remember the place value order: Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands.
Tip 2: Use commas to separate periods: 357,428 (not 357428).
Tip 3: Hyphenate compound numbers from 21-99: twenty-one, thirty-five, etc.
Tip 4: Practice with place value charts to visualize the positions.
Common errors: Confusing place values, forgetting commas, misreading zeros, not hyphenating compound numbers, mispronouncing large numbers.
Real-world applications: Reading population counts, distances, money amounts, scores, measurements, statistics, and any large numbers encountered in daily life.
Place value rules:

• Each position is 10 times the position to its right

• Comma placement: Every three digits from right to left

• Period names: Ones, Thousands, Millions

• Compound numbers: Use hyphens (twenty-one, thirty-five)

• Zero handling: Zeros in middle positions are included in reading

• Value calculation: Digit × Place value = Digit's contribution

Solution: Exercises 4 to 5
4 Comparing large numbers
Exercise 4
Compare 523,741 and 523,809. Which number is greater? Explain your reasoning.
Definition:

Comparing large numbers: Determining which of two or more large numbers is greater by comparing digits from left to right, starting with the highest place value.

Numbers
523,741 vs 523,809
Compare digits
5=5, 2=2, 3=3, 7<8
Result
523,741 < 523,809
Step 1: Align the numbers by place value

523,741

523,809

Step 2: Compare from left to right

Hundred thousands: 5 = 5, continue comparing

Step 3: Compare ten thousands

2 = 2, continue comparing

Step 4: Compare thousands

3 = 3, continue comparing

Step 5: Compare hundreds

7 < 8, so 523,741 < 523,809

Step 6: State the comparison

523,809 is greater than 523,741

523,809 is greater
Final answer:

523,809 is greater than 523,741 because in the hundreds place, 8 > 7.

Applied rules:

• Left-to-right comparison: Start with the highest place value

• Digit-by-digit: Compare corresponding digits in the same place

• Stop when different: First differing digit determines the comparison

5 Problem-solving with large numbers
Exercise 5
A city has a population of 742,583. Another city has a population of 742,601. How many more people live in the second city?
Definition:

Large number subtraction: Finding the difference between two large numbers by aligning place values and subtracting corresponding digits, sometimes requiring regrouping.

Larger population
742,601
Smaller population
742,583
Difference
742,601 - 742,583 = 18
Step 1: Identify the larger and smaller numbers

742,601 > 742,583

Step 2: Set up the subtraction

742,601 - 742,583

Step 3: Align by place value

742,601

- 742,583

Step 4: Subtract from right to left

Ones: 1 - 3 (need to borrow)

Tens: 0 - 8 (need to borrow)

Hundreds: 6 - 5 = 1 (after borrowing)

Step 5: Perform the calculation

742,601 - 742,583 = 18

Step 6: State the answer

The second city has 18 more people

18 more people
Final answer:

The second city has 18 more people than the first city.

Applied rules:

• Place alignment: Align numbers by place value before subtracting

• Regrouping: Borrow from higher place values when needed

• Context: Interpret the difference in the problem's context

Complete Summary: Reading Numbers Up to 1,000,000
Digit × Place Value = Digit's Contribution
Place Value Formula
Key definitions:

Place value: The value of a digit based on its position in a number. Each position represents a power of 10, with each position being 10 times the value of the position to its right.

Period: A group of three digits in a number, separated by commas. The main periods are ones, thousands, and millions.

Expanded form: Writing a number as the sum of the values of each digit (e.g., 357,428 = 300,000 + 50,000 + 7,000 + 400 + 20 + 8).

Standard form: Writing a number using digits (e.g., 357,428).

Word form: Writing a number using words (e.g., three hundred fifty-seven thousand four hundred twenty-eight).

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

Compound numbers: Numbers from 21-99 that contain hyphens when written in words (e.g., twenty-one, thirty-five).

Complete number reading methodology:
  1. Identify periods: Separate the number into groups of three digits using commas
  2. Determine place values: Know the value of each position (ones, tens, hundreds, thousands, ten thousands, hundred thousands)
  3. Read each period: Read the digits in each period as if they were in the ones period
  4. Add period names: Include "thousand" for the thousands period
  5. Combine periods: Read the entire number as a whole
  6. Apply conventions: Use hyphens for compound numbers, include zeros appropriately
Tip 1: Remember the place value order: Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands.
Tip 2: Use commas to separate periods: 357,428 (not 357428).
Tip 3: Hyphenate compound numbers from 21-99: twenty-one, thirty-five, etc.
Tip 4: Practice with place value charts to visualize the positions.
Tip 5: When comparing, start from the leftmost digit and work right until you find a difference.
Common errors: Confusing place values, forgetting commas, misreading zeros, not hyphenating compound numbers, mispronouncing large numbers, comparing from right to left instead of left to right.
Real-world applications: Reading population counts, distances, money amounts, scores, measurements, statistics, scientific data, and any large numbers encountered in daily life.
Key place value principles:

• Each position is 10 times the value of the position to its right

• Comma placement: Every three digits from right to left

• Period names: Ones, Thousands, Millions

• Compound numbers: Use hyphens (twenty-one, thirty-five)

• Zero handling: Zeros in middle positions are included in reading

• Value calculation: Digit × Place value = Digit's contribution

• Comparison: Start from leftmost digit, compare corresponding positions

Visual Guide to Reading Numbers Up to 1,000,000

🔢
Place Value Chart

Hundred Thousands: 100,000

Ten Thousands: 10,000

Thousands: 1,000

Hundreds: 100

Tens: 10

Ones: 1

Example: 473,829

Number Names

Separate periods with commas

Read each period separately

Add "thousand" for thousands period

Hyphenate compound numbers (21-99)

Example: 642,817 = Six hundred forty-two thousand eight hundred seventeen

Expanded Form

Break into place values

Each digit × its place value

Add all parts together

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

Comparison

Compare from left to right

Start with highest place value

First differing digit determines comparison

Example: 523,741 < 523,809 (because 7 < 8 in hundreds place)

Questions & Answers

Question: I get confused about which place value is which. How can I remember the order of place values?

Answer: Here's a helpful way to remember the place value order from right to left:

  • Ones (1)
  • Tens (10)
  • Hundreds (100)
  • Thousands (1,000)
  • Ten Thousands (10,000)
  • Hundred Thousands (100,000)

Remember: Each place value is 10 times the one to its right. You can also think of it as adding a zero each time you move left: 1, 10, 100, 1,000, 10,000, 100,000.

Practice by writing numbers and labeling each digit with its place value to build familiarity!

Question: When do I need to use hyphens when writing numbers in words? I always forget.

Answer: Use hyphens for compound numbers from 21 to 99 (except multiples of 10 like thirty, forty, etc.). Specifically:

  • Hyphenate numbers like: twenty-one, thirty-five, forty-eight, fifty-nine, sixty-three, seventy-six, eighty-two, ninety-four
  • DO NOT hyphenate: twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety
  • DO NOT hyphenate: one hundred, two hundred, etc.

Example: 427 = four hundred twenty-seven (hyphenate "twenty-seven" because it's between 21-99)

Example: 430 = four hundred thirty (no hyphen because thirty is a multiple of 10)

Remember: Only hyphenate the tens and ones when they form a compound number!

Question: When comparing large numbers, should I start from the left or the right? I sometimes get confused.

Answer: Always compare large numbers from LEFT to RIGHT, starting with the highest place value. This is because the leftmost digits have the greatest value:

  • Compare the leftmost digits first (hundred thousands, if both numbers have them)
  • If they're the same, move to the next digit to the right
  • Continue until you find digits that are different
  • The number with the larger digit in the first different place is the greater number

Example: Comparing 523,741 and 523,809

- Hundred thousands: 5 = 5 (same, continue)

- Ten thousands: 2 = 2 (same, continue)

- Thousands: 3 = 3 (same, continue)

- Hundreds: 7 < 8 (different! So 523,741 < 523,809)

Remember: Start with the biggest place value and work your way right!