Write an Equation for 45,603: Multiple Representation Challenge

Q: Why do we include 0×10 in the expanded form?

Even though zero times anything equals zero, we include 0×10 to show that the tens place exists but has no value. This helps maintain the complete place value structure and shows every position clearly.

Q: How do I remember the order of place values?

Think of it as powers of 10: ones (10⁰), tens (10¹), hundreds (10²), thousands (10³), ten-thousands (10⁴). Each place is 10 times bigger than the place to its right!

Q: What if I wrote the digits in the wrong order?

Always double-check by reading the number left to right: 45,603 means 4 ten-thousands, 5 thousands, 6 hundreds, 0 tens, 3 ones. Match each digit to its correct place value position.

Q: Can I skip writing terms with zero?

For complete expanded form, include all place values even with zero. However, in simplified form, you can write $ 4×10,000 + 5×1,000 + 6×100 + 3 $ since 0×10 = 0.

Q: How do I check if my expanded form is correct?

Calculate each term separately: 4×10,000 = 40,000, 5×1,000 = 5,000, 6×100 = 600, 0×10 = 0, 3×1 = 3. Then add them all: 40,000 + 5,000 + 600 + 0 + 3 = 45,603 ✓

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Choose an equation for the number 45,603.

2

Step-by-step solution

To solve this problem, we need to express the number 45,603 clearly through its decomposition using place values from the decimal system. Let's follow these structured steps:

Step 1: Identify place values and digits.
- The digit in the ten-thousands place is 4.
- The digit in the thousands place is 5.
- The digit in the hundreds place is 6.
- The digit in the tens place is 0.
- The digit in the units place is 3.
Step 2: Write the number in expanded form using the identified place values.
- By following the place value, we express the number as $4 \times 10,000 + 5 \times 1,000 + 6 \times 100 + 0 \times 10 + 3 \times 1$ .
Step 3: Verify the expression matches one of the choices provided.
- Compare this decomposition with the given answer choices to find a match.

The correct decomposition according to the calculation matches choice 4, which is $4 \times 10,000 + 5 \times 1,000 + 6 \times 100 + 0 \times 10 + 3 \times 1$ .

Therefore, the equation that represents 45,603 is $45,603 = 4 \times 10,000 + 5 \times 1,000 + 6 \times 100 + 0 \times 10 + 3 \times 1$ .

3

Final Answer

$45,603=4\times10,000+5\times1,000+6\times100+0\times10+3\times1$

Key Points to Remember

Essential concepts to master this topic

Place Values: Each digit position represents powers of ten (10,000s, 1,000s, 100s, 10s, 1s)
Expanded Form: Write 45,603 = 4×10,000 + 5×1,000 + 6×100 + 0×10 + 3×1
Verification: Add up all terms: 40,000 + 5,000 + 600 + 0 + 3 = 45,603 ✓

Common Mistakes

Avoid these frequent errors

Mixing up digit positions when writing expanded form
Don't write 4 in the thousands place when it belongs in ten-thousands = wrong equation like 3×10,000 + 0×1,000 + 6×100 + 5×10 + 4×1! This scrambles the digits and creates a completely different number. Always read from left to right: ten-thousands, thousands, hundreds, tens, ones.

Practice Quiz

Test your knowledge with interactive questions

What number do the units shown below represent?

Write the units in the place value chart and convert into a number.

FAQ

Everything you need to know about this question

Why do we include 0×10 in the expanded form?

+

Even though zero times anything equals zero, we include 0×10 to show that the tens place exists but has no value. This helps maintain the complete place value structure and shows every position clearly.

How do I remember the order of place values?

+

Think of it as powers of 10: ones (10⁰), tens (10¹), hundreds (10²), thousands (10³), ten-thousands (10⁴). Each place is 10 times bigger than the place to its right!

What if I wrote the digits in the wrong order?

+

Always double-check by reading the number left to right: 45,603 means 4 ten-thousands, 5 thousands, 6 hundreds, 0 tens, 3 ones. Match each digit to its correct place value position.

Can I skip writing terms with zero?

+

For complete expanded form, include all place values even with zero. However, in simplified form, you can write $4×10,000 + 5×1,000 + 6×100 + 3$ since 0×10 = 0.

How do I check if my expanded form is correct?

+

Calculate each term separately: 4×10,000 = 40,000, 5×1,000 = 5,000, 6×100 = 600, 0×10 = 0, 3×1 = 3. Then add them all: 40,000 + 5,000 + 600 + 0 + 3 = 45,603 ✓

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Write an Equation for 45,603: Multiple Representation Challenge

Place Value Decomposition with Zero Digits

❤️ Continue Your Math Journey!

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do we include 0×10 in the expanded form?

How do I remember the order of place values?

What if I wrote the digits in the wrong order?

Can I skip writing terms with zero?

How do I check if my expanded form is correct?

🌟 Unlock Your Math Potential

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