Place Value Problem: Find the Number 4-2-8 Using Digit Positions

Q: What's the difference between 428 and 248?

The position makes all the difference! In 428, the 4 is in the hundreds place (worth 400). In 248, the 4 is in the units place (worth only 4). Same digit, completely different value!

Q: Why can't I just write the digits in any order?

Because place value matters! The position of each digit determines its value. The hundreds digit contributes 100 times more than the units digit to the final number.

Q: How do I remember which position is which?

Think from right to left: units (ones), tens, hundreds. Or remember: the rightmost digit is always the units place, and each position to the left is 10 times bigger!

Q: Can I use the formula method for bigger numbers too?

Absolutely! The formula $ \text{Number} = \text{digit} \times \text{place value} $ works for any size number. Just extend it: thousands, ten-thousands, and so on.

Place Value Construction with Three-Digit Numbers

My hundreds digit is 4, my tens digit is 2, and my units digit is 8.

What number am I?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

My hundreds digit is 4, my tens digit is 2, and my units digit is 8.

What number am I?

Step-by-step solution

To solve the problem, we'll determine the number formed by the given digits based on their respective positions in the number:

Step 1: Identify the positions of the digits.
- Hundreds digit is 4.
- Tens digit is 2.
- Units digit is 8.
Step 2: Use the decimal structure formula to form the number.
- Number = $100 \times 4 + 10 \times 2 + 1 \times 8$
Step 3: Perform the multiplication and sum:
- $100 \times 4 = 400$
- $10 \times 2 = 20$
- $1 \times 8 = 8$
Step 4: Add these values together:
- $400 + 20 + 8 = 428$

Therefore, the number we are looking for is $428$ .

Final Answer

$428$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Each position represents a power of ten (hundreds, tens, units)
Construction Method: Multiply each digit by its place value: $4×100 + 2×10 + 8×1$
Verification: Check that your number has the correct digit in each position ✓

Common Mistakes

Avoid these frequent errors

Writing digits in wrong order
Don't just put the digits together as 248 or 824 without considering place value! This ignores which position each digit belongs in. Always place each digit in its specified position: hundreds=4, tens=2, units=8 gives 428.

Practice Quiz

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What number do the blue squares below represent?

FAQ

Everything you need to know about this question

What's the difference between 428 and 248?

The position makes all the difference! In 428, the 4 is in the hundreds place (worth 400). In 248, the 4 is in the units place (worth only 4). Same digit, completely different value!

Why can't I just write the digits in any order?

Because place value matters! The position of each digit determines its value. The hundreds digit contributes 100 times more than the units digit to the final number.

How do I remember which position is which?

Think from right to left: units (ones), tens, hundreds. Or remember: the rightmost digit is always the units place, and each position to the left is 10 times bigger!

What if I mix up the hundreds and units digits?

You'll get a completely different number! If hundreds=4 and units=8, mixing them up gives you hundreds=8 and units=4, which makes 824 instead of 428 - a difference of 396!

Can I use the formula method for bigger numbers too?

Absolutely! The formula $\text{Number} = \text{digit} \times \text{place value}$ works for any size number. Just extend it: thousands, ten-thousands, and so on.

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