Solved Exercises on Expanded Form to 99 in Grade 4

Master expanded form to 99: place value decomposition, digit representation, and number composition through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic place value decomposition
Exercise 1
Write the expanded form of: 47
Definition:

Expanded form: Writing a number to show the value of each digit based on its place value (tens and ones).

Place Value Method:
  1. Identify the place value of each digit (tens, ones)
  2. Multiply each digit by its place value
  3. Add all the products together
Number
47
Expanded
40 + 7
Step 1: Identify place values

4 is in tens place (4 × 10 = 40)

7 is in ones place (7 × 1 = 7)

Step 2: Write as addition of place values

47 = 40 + 7

Step 3: Verify the expansion

40 + 7 = 47 ✓

47 = 40 + 7
Final answer:

47 = 40 + 7

Applied rules:

• Place Value: Each digit has a specific value based on position

• Position System: Right to left: ones, tens

• Decomposition: Break down into parts that sum to original number

2 Expanded form with zero in ones place
Exercise 2
Write the expanded form of: 80
Definition:

Zero in expanded form: Even zeros represent their place value (e.g., 0 ones = 0)

Number
80
Expanded
80 + 0
Simplified
80
Step 1: Identify place values

8 is in tens place (8 × 10 = 80)

0 is in ones place (0 × 1 = 0)

Step 2: Write as addition of place values

80 = 80 + 0

Step 3: Simplify by removing zero term

80 = 80

80 = 80 + 0
Final answer:

80 = 80 + 0 (or simply 80)

Applied rules:

• Zero Place Value: Zeros still represent their position's value

• Simplification: Adding zero doesn't change the sum

• Place Recognition: Identify all positions even with zeros

3 Converting expanded to standard form
Exercise 3
Write in standard form: 50 + 3
Definition:

Standard form: The regular way we write numbers without showing place values

Expanded
50 + 3
Standard
53
Step 1: Identify each place value

50 → 5 in tens place

3 → 3 in ones place

Step 2: Combine the digits in order

Tens: 5, Ones: 3

So we get 53

Step 3: Verify by converting back to expanded form

53 = 50 + 3 ✓

Step 4: Final answer

50 + 3 = 53

50 + 3 = 53
Final answer:

50 + 3 = 53

Applied rules:

• Place Value Addition: Sum all expanded parts to get standard form

• Digit Placement: Each part corresponds to a specific place

• Verification: Convert back to ensure accuracy

Place Value System and Expanded Form Rules (0-99)
\(47 = 40 + 7\)
Expanded Form Example
Ones Place
\(d \times 1\)
Digit × 1
Tens Place
\(d \times 10\)
Digit × 10
Key definitions:

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

Expanded Form: Writing a number as the sum of the value of each digit

Standard Form: The regular way we write numbers

Tens: Groups of 10 (10, 20, 30, etc.)

Ones: Single units (1, 2, 3, etc.)

Complete methodology:
  1. Identify positions: Recognize tens and ones places
  2. Determine values: Multiply each digit by its place value (10 or 1)
  3. Express as sum: Write the addition of all place values
  4. Verify: Check that the sum equals the original number
Tip 1: Remember the order: Tens, then Ones (TO).
Tip 2: Zeros in expanded form can be omitted in the final answer.
Tip 3: Always verify by adding the expanded parts to get the original number.
Tip 4: Use base-10 rods and unit blocks to visualize place values.
Common errors: Forgetting place values, misplacing digits, ignoring zeros.
Memory aid: Use "TO" (Tens, Ones) to remember the order.
Formulas to know by heart:

• Place value: Digit × Position value (1, 10)

• Expanded form: Sum of all place values

• Standard form: Regular number notation

• Verification: Sum of expanded parts = Original number

Solution: Exercises 4 to 5
4 Word problem application
Exercise 4
Tom has 63 marbles. Write this number in expanded form and explain what each part represents.
Definition:

Word problem conversion: Translate real-world quantities into mathematical forms

Number
63
Expanded
60 + 3
Step 1: Identify each digit's place value

6 is in tens place (6 × 10 = 60)

3 is in ones place (3 × 1 = 3)

Step 2: Write in expanded form

63 = 60 + 3

Step 3: Interpret the meaning

60: Six tens (six groups of 10 marbles = 60 marbles)

3: Three ones (three single marbles)

Total: 60 + 3 = 63 marbles

63 = 60 + 3
Final answer:

63 = 60 + 3

This means Tom has 6 tens of marbles (60 marbles) and 3 single marbles.

Applied rules:

• Real-world application: Connect math to practical situations

• Place value understanding: Each digit represents a specific quantity

• Context interpretation: Explain what each part means

5 Multiple representations
Exercise 5
Show the number 94 in three different ways: standard form, expanded form, and word form.
Definition:

Multiple representations: Same number shown in different mathematical forms

Standard
94
Expanded
90 + 4
Word
Ninety-four
Step 1: Standard form

94 (regular number notation)

Step 2: Expanded form

94 = 90 + 4

(9×10) + (4×1)

Step 3: Word form

Read the number aloud: Ninety-four

Step 4: Verify all forms are equivalent

90 + 4 = 94 ✓

Standard: 94
Expanded: 90 + 4
Word: Ninety-four
Final answer:

Standard form: 94

Expanded form: 90 + 4

Word form: Ninety-four

Applied rules:

• Number equivalence: All forms represent the same quantity

• Conversion skills: Practice moving between different representations

• Verification: Confirm all forms equal the same value

Complete Summary: Expanded Form to 99
\(d_t \times 10 + d_o \times 1\)
General Expanded Form Formula (0-99)
Key definitions:

Place Value: The value of a digit based on its position in a number (ones, tens)

Expanded Form: A number expressed as the sum of the value of each digit multiplied by its place value

Standard Form: The usual way we write numbers (e.g., 47)

Word Form: Numbers written out in words (e.g., forty-seven)

Tens Place: The second digit from the right, representing groups of 10

Ones Place: The rightmost digit, representing single units

Complete methodology:
  1. Position identification: Identify the tens and ones place (right to left)
  2. Multiplication: Multiply each digit by its corresponding place value (10 or 1)
  3. Addition: Express the number as the sum of all place values
  4. Verification: Add the expanded parts to confirm they equal the original number
Tip 1: Use the acronym TO (Tens, Ones) to remember place value order.
Tip 2: Draw a place value chart to organize digits before expanding.
Tip 3: Always include zeros in your place value analysis, even if they simplify out.
Tip 4: Practice reading numbers aloud to reinforce place value understanding.
Common errors: Misplacing digits, forgetting place values, confusing tens with ones.
Memory aids: Use base-10 blocks, draw charts, count positions from right to left starting at 0.
Formulas and Rules to Know:

• Place Value Pattern: ..., 100, 10, 1

• Expanded Form: Sum of (digit × place value)

• Zero Rule: Zeros contribute 0 to the sum but indicate position

• Verification: Expanded parts must sum to original number

• Range: For numbers 0-99, only tens and ones places apply

Place Value Visualization: Numbers 0-99
Exercise 6: Understanding Place Values
Consider the following numbers and their place value breakdowns:
23 = 20 + 3
70 = 70 + 0
45 = 40 + 5

Analysis: The chart shows how numbers decompose into their place value components.

  • 23 = 2×10 + 3×1 (Two tens and three ones)
  • 70 = 7×10 + 0×1 (Seven tens and zero ones)
  • 45 = 4×10 + 5×1 (Four tens and five ones)

Questions & Answers

Question: I don't understand why we need to learn expanded form. Why can't we just write numbers normally?

Answer: Great question! Expanded form is crucial for understanding how our number system works:

  • It helps you understand place value - knowing that in 47, the 4 represents 40, not just 4
  • It builds a foundation for addition and subtraction with regrouping
  • It prepares you for working with larger numbers later
  • It makes it easier to compare numbers and understand their magnitude

Think of it like understanding how money works: $4.70 means 4 dollars (400 cents) and 70 cents. Expanded form does the same thing for whole numbers!

Question: My child gets confused when there are zeros in the number like 80. How do I explain the expanded form?

Answer: Here's a helpful approach for numbers with zeros:

  • Use a place value chart to show every position: Tens | Ones
  • Write 80 in the chart: 8 in tens, 0 in ones
  • Even though the ones digit is 0, it still represents 0 ones = 0
  • So: 80 = 80 + 0, which can be simplified to just 80

You can also use manipulatives like base-10 rods: 8 ten-rods (80) and 0 unit blocks (0). The absence of unit blocks still represents 0 ones!

The zero keeps the 8 in the correct place!

Question: What's the best way to check if my expanded form is correct?

Answer: Here are effective verification methods:

  • Add up the expanded parts: If you wrote 47 as 40 + 7, add them: 40 + 7 = 47 ✓
  • Count the digits: Make sure you have one term for each digit in the original number
  • Check place values: Ensure each digit is multiplied by the correct place value (10 or 1)
  • Use estimation: The larger term should be close to the original number

For example, with 47: The largest term (40) is close to 47, which makes sense. The sum 40 + 7 = 47 confirms the answer is correct!