Number Decomposition: Breaking Down 57.5 into Its Components

Q: Why can't I just write 57 + 0.5?

While $ 57 + 0.5 $ equals 57.5, it doesn't show the place value breakdown. True decomposition separates each digit by its place: tens, ones, and tenths.

Q: What does the 0.5 really mean?

The 0.5 means five-tenths or half of one whole. It's the same as $ \frac{5}{10} $ or $ \frac{1}{2} $.

Q: Can I decompose any decimal number this way?

Absolutely! Every decimal can be broken down by place value. For example, 123.45 = 100 + 20 + 3 + 0.4 + 0.05.

Q: What if there are more decimal places?

Just continue the pattern! For 57.52, you'd have: 50 + 7 + 0.5 + 0.02 (fifty + seven + five-tenths + two-hundredths).

Place Value Decomposition with Decimal Numbers

Choose the correct decomposition of the number 57.5.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Break down the number

00:05 Identify the appropriate operation for each digit

00:25 Place each digit with its multiplication and add

00:45 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the correct decomposition of the number 57.5.

Step-by-step solution

To solve this problem, we will decompose the number 57.5 by identifying the place value of each digit:

First, note that the '5' in 57.5 is in the tens place, representing $5 \times 10 = 50$ .
The '7' is in the ones place, contributing $7 \times 1 = 7$ .
The '.5' is in the tenths place, which corresponds to $0.5$ .

By adding these components together, we have:

$50 + 7 + 0.5$ .

Thus, the decomposition of 57.5 is $50+7+0.5$ .

Final Answer

$50+7+0.5$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Each digit represents its value times its position
Technique: Break 57.5 into tens (50) + ones (7) + tenths (0.5)
Check: Add components back together: 50 + 7 + 0.5 = 57.5 ✓

Common Mistakes

Avoid these frequent errors

Treating decimal places like whole number places
Don't write 0.5 as just 5 in your decomposition = wrong total of 62! The decimal point shows tenths, not ones. Always include 0.5 to represent five-tenths, not five ones.

Practice Quiz

Test your knowledge with interactive questions

Which figure represents 0.1?

FAQ

Everything you need to know about this question

Why can't I just write 57 + 0.5?

While $57 + 0.5$ equals 57.5, it doesn't show the place value breakdown. True decomposition separates each digit by its place: tens, ones, and tenths.

What does the 0.5 really mean?

The 0.5 means five-tenths or half of one whole. It's the same as $\frac{5}{10}$ or $\frac{1}{2}$ .

How do I know which place each digit is in?

Start from the decimal point and work outward:

Left of decimal: ones, tens, hundreds...
Right of decimal: tenths, hundredths, thousandths...

Can I decompose any decimal number this way?

Absolutely! Every decimal can be broken down by place value. For example, 123.45 = 100 + 20 + 3 + 0.4 + 0.05.

What if there are more decimal places?

Just continue the pattern! For 57.52, you'd have: 50 + 7 + 0.5 + 0.02 (fifty + seven + five-tenths + two-hundredths).

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