Solve: 1×100,000 + 2×10,000 + 4×1,000 + 9×1 in Standard Form

Q: Why do we multiply each digit by a different number?

Each position in a number represents a different place value! The digit 1 in the hundred-thousands place is worth 100,000 times more than 1 in the ones place.

Q: What if there's a zero in the expansion?

If a place value has zero, like 0×100, it equals zero and doesn't affect the final sum. Just skip that term or write it as 0.

Q: How do I remember which place value goes where?

Start from the right with ones (1), then move left: tens (10), hundreds (100), thousands (1,000), etc. Each place is 10 times bigger than the one before it.

Q: What's the difference between expanded form and standard form?

Expanded form shows the addition of place values like $ 1×100,000 + 2×10,000... $ while standard form is the final number: 124,009.

Place Value Expansion with Multiple Powers

$1\times100,000+2\times10,000+4\times1,000+9\times1=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$1\times100,000+2\times10,000+4\times1,000+9\times1=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Multiply each digit by the appropriate power of ten.
Step 2: Sum the resulting values to find the final result.

Let's proceed with the calculations:
Step 1: Calculate each component of the expression:

$1 \times 100,000 = 100,000$
$2 \times 10,000 = 20,000$
$4 \times 1,000 = 4,000$
$9 \times 1 = 9$

Step 2: Add all the computed values together:

100,000 + 20,000 + 4,000 + 9 = 124,009

Therefore, the solution to the problem is $124,009$ .

Final Answer

$124,009$

Key Points to Remember

Essential concepts to master this topic

Rule: Each digit multiplies by its place value power of ten
Technique: Calculate 4×1,000 = 4,000 then add all products together
Check: Count digits in final answer matches highest place value ✓

Common Mistakes

Avoid these frequent errors

Adding digits instead of multiplying by place values
Don't just add 1+2+4+9 = 16! This ignores place values completely and gives a tiny wrong answer. Always multiply each digit by its corresponding place value first, then add the products.

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 a different number?

Each position in a number represents a different place value! The digit 1 in the hundred-thousands place is worth 100,000 times more than 1 in the ones place.

What if there's a zero in the expansion?

If a place value has zero, like 0×100, it equals zero and doesn't affect the final sum. Just skip that term or write it as 0.

How do I remember which place value goes where?

Start from the right with ones (1), then move left: tens (10), hundreds (100), thousands (1,000), etc. Each place is 10 times bigger than the one before it.

Can I work from left to right instead of right to left?

Absolutely! The order doesn't matter when adding. You can calculate $100,000 + 20,000 + 4,000 + 9$ in any order and get the same result.

What's the difference between expanded form and standard form?

Expanded form shows the addition of place values like $1×100,000 + 2×10,000...$ while standard form is the final number: 124,009.

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