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

If you use all of the units shown below and place them in the table, then what number do they make?

Write the values 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

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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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