Number Decomposition: Breaking Down 300.6 into Place Values

Q: Why can't I write 0.6 as just 6?

Because 0.6 and 6 are completely different values! 0.6 means 6 tenths, while 6 means 6 ones. The decimal point shows the place value and is essential for correct decomposition.

Q: What's the difference between the whole part and decimal part?

The whole part comes before the decimal point (300 in 300.6), and the decimal part comes after it (0.6). Think of it as dollars and cents: $300.60 has 300 dollars and 60 cents.

Q: Do I always need to include the zero before the decimal?

Yes, absolutely! Writing 0.6 instead of just .6 makes it clearer and prevents mistakes. The zero shows there are no ones in the decimal part.

Q: Can I break down the whole number part further?

Yes! You could write 300.6 as $ 300 + 0.6 $ or even as $ 200 + 100 + 0.6 $. But the question asks for the basic decomposition into whole and decimal parts.

Q: How do I check if my decomposition is correct?

Simply add your parts back together! If 300 + 0.6 = 300.6, then your decomposition is correct. This is the best way to verify your answer.

Decimal Decomposition with Whole and Fractional Parts

Choose the correct decomposition of the number 300.6.

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Step-by-step video solution

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00:00 Break down the number

00:09 Identify the appropriate operation for each digit

00:44 And this is the solution to the question

Step-by-step written solution

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Understand the problem

Choose the correct decomposition of the number 300.6.

Step-by-step solution

The task is to decompose 300.6 into its constituent parts based on its decimal structure.

The number 300.6 consists of:

300, which is the whole number (integer) part.
0.6, which is the fractional (decimal) part.

To decompose 300.6 correctly, we must express it as the sum of these two components:

$300.6 = 300 + 0.6$

Now, let's evaluate the provided answer choices:

Choice 1: $300 + 0.6$ - This correctly represents the decomposition.
Choice 2: $300 + 6$ - This incorrectly assumes 0.6 is just 6.
Choice 3: $30 + 306$ - This misrepresents both the integer and the decimal parts.
Choice 4: $30 + 0.6$ - This only partially decomposes the integer incorrectly.

Therefore, the correct decomposition of 300.6 is choice 1: $300 + 0.6$ .

Final Answer

$300+0.6$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Separate whole numbers from decimal parts clearly
Technique: Split 300.6 into 300 (whole) + 0.6 (decimal)
Check: Add parts together: 300 + 0.6 = 300.6 ✓

Common Mistakes

Avoid these frequent errors

Dropping the decimal point from fractional parts
Don't write 0.6 as just 6 when decomposing = changes the actual value! This makes 300 + 6 = 306, not 300.6. Always keep the decimal point to preserve place values.

Practice Quiz

Test your knowledge with interactive questions

Determine the numerical value of the shaded area:

FAQ

Everything you need to know about this question

Why can't I write 0.6 as just 6?

Because 0.6 and 6 are completely different values! 0.6 means 6 tenths, while 6 means 6 ones. The decimal point shows the place value and is essential for correct decomposition.

What's the difference between the whole part and decimal part?

The whole part comes before the decimal point (300 in 300.6), and the decimal part comes after it (0.6). Think of it as dollars and cents: $300.60 has 300 dollars and 60 cents.

Do I always need to include the zero before the decimal?

Yes, absolutely! Writing 0.6 instead of just .6 makes it clearer and prevents mistakes. The zero shows there are no ones in the decimal part.

Can I break down the whole number part further?

Yes! You could write 300.6 as $300 + 0.6$ or even as $200 + 100 + 0.6$ . But the question asks for the basic decomposition into whole and decimal parts.

How do I check if my decomposition is correct?

Simply add your parts back together! If 300 + 0.6 = 300.6, then your decomposition is correct. This is the best way to verify your answer.

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