Solve: Converting 154,300 Using Expanded Notation with Powers of 10

Q: Why do we multiply each digit by its place value?

Each position in a number represents a different power of 10. The digit 5 in the ten-thousands place actually means $ 5 \times 10,000 = 50,000 $, not just 5!

Q: What happens when there's a 0 in the expanded form?

When you multiply by 0, you get 0! So $ 0 \times 1 = 0 $ contributes nothing to the final sum. Don't forget to include it in your addition though!

Q: How do I remember the place values?

Start from the right with ones (1), then move left: tens (10), hundreds (100), thousands (1,000), ten-thousands (10,000), hundred-thousands (100,000). Each place is 10 times bigger than the previous!

Q: Is there a faster way to solve this?

Once you understand place values, you can directly read the number! The expanded form $ 1 \times 100,000 + 5 \times 10,000 + 4 \times 1,000 + 3 \times 100 + 0 \times 1 $ simply writes out 154,300.

Expanded Notation with Place Value Addition

$1\times100,000+5\times10,000+4\times1,000+3\times100+0\times1=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$1\times100,000+5\times10,000+4\times1,000+3\times100+0\times1=$

Step-by-step solution

To solve this problem, we will evaluate the sum of the expression given by:

$1 \times 100,000 + 5 \times 10,000 + 4 \times 1,000 + 3 \times 100 + 0 \times 1$

Let's follow these detailed steps:

Step 1: Identify each digit and its respective place value.
- 1 in the hundred-thousands place
- 5 in the ten-thousands place
- 4 in the thousands place
- 3 in the hundreds place
- 0 in the ones place
Step 2: Multiply each digit by its place value:
- $1 \times 100,000 = 100,000$
- $5 \times 10,000 = 50,000$
- $4 \times 1,000 = 4,000$
- $3 \times 100 = 300$
- $0 \times 1 = 0$
Step 3: Add these results together:
- $100,000 + 50,000 + 4,000 + 300 + 0 = 154,300$

Therefore, the solution to the problem is $154,300$ .

Comparing with the provided answer choices, choice 4 $(154,340)$ is indeed the correct answer.

Final Answer

$154,340$

Key Points to Remember

Essential concepts to master this topic

Place Value: Each digit has a specific position value like 10,000s or 100s
Technique: Multiply each digit by its place value: $5 \times 10,000 = 50,000$
Check: Add all products to get final number: 100,000 + 50,000 + 4,000 + 300 + 0 = 154,300 ✓

Common Mistakes

Avoid these frequent errors

Adding digits without considering place values
Don't just add 1 + 5 + 4 + 3 + 0 = 13! This ignores place values completely and gives a tiny incorrect answer. Always multiply each digit by its place value first, then add all the products together.

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 multiply each digit by its place value?

Each position in a number represents a different power of 10. The digit 5 in the ten-thousands place actually means $5 \times 10,000 = 50,000$ , not just 5!

What happens when there's a 0 in the expanded form?

When you multiply by 0, you get 0! So $0 \times 1 = 0$ contributes nothing to the final sum. Don't forget to include it in your addition though!

How do I remember the place values?

Start from the right with ones (1), then move left: tens (10), hundreds (100), thousands (1,000), ten-thousands (10,000), hundred-thousands (100,000). Each place is 10 times bigger than the previous!

Why doesn't my answer match any of the choices?

Double-check your multiplication! Make sure you're using the correct place values. For example, $4 \times 1,000 = 4,000$ , not 400 or 40,000.

Is there a faster way to solve this?

Once you understand place values, you can directly read the number! The expanded form $1 \times 100,000 + 5 \times 10,000 + 4 \times 1,000 + 3 \times 100 + 0 \times 1$ simply writes out 154,300.

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