Compare Decimals: Is 0.250 Equal to 0.0250?

Q: Why don't the trailing zeros in 0.250 matter but the leading zero in 0.0250 does?

Trailing zeros after the last significant digit don't change value (0.25 = 0.250), but leading zeros after the decimal point shift digits to smaller place values, making the number smaller.

Q: How can I quickly tell which decimal is larger?

Compare digits from left to right after the decimal point. 0.250 has 2 in the tenths place, while 0.0250 has 0 in tenths and 2 in hundredths, so 0.250 is larger.

Q: Can I just remove all the zeros to compare?

No! You can only remove trailing zeros (at the end). Leading zeros after the decimal point are crucial for place value and cannot be removed.

Q: How do I remember the difference between these types of zeros?

Think of it like money: $2.50 = $2.500 (trailing zeros don't matter), but $2.50 ≠ $0.250 (leading zeros after decimal create different amounts).

Decimal Comparison with Place Value Analysis

Are the fractions equal?

$0.250 \, \stackrel{?}{=} \, 0.0250$

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Step-by-step written solution

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Understand the problem

Are the fractions equal?

$0.250 \, \stackrel{?}{=} \, 0.0250$

Step-by-step solution

To determine if the fractions are equal, compare the two decimal numbers:

$0.250$ and $0.0250$ .

The placement of zeros can affect the value, but in this case:

$0.250$ is equivalent to $\frac{250}{1000}$ , which simplifies to $\frac{1}{4}$ .

$0.0250$ is equivalent to $\frac{250}{10000}$ , which simplifies to $\frac{1}{40}$ .

The fractions $\frac{1}{4}$ and $\frac{1}{40}$ are not equal, therefore:

$0.250 \neq 0.0250$

Final Answer

$\neq$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Each decimal position has ten times greater value
Technique: Convert to fractions: 0.250 = 250/1000, 0.0250 = 250/10000
Check: Simplify fractions: 1/4 ≠ 1/40, so decimals are not equal ✓

Common Mistakes

Avoid these frequent errors

Ignoring leading zeros after decimal point
Don't think 0.250 = 0.0250 because they have the same digits = wrong comparison! Leading zeros after the decimal point shift all digits to smaller place values, changing the actual value. Always count decimal places carefully from the decimal point.

Practice Quiz

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Which decimal number is greater?

FAQ

Everything you need to know about this question

Why don't the trailing zeros in 0.250 matter but the leading zero in 0.0250 does?

Trailing zeros after the last significant digit don't change value (0.25 = 0.250), but leading zeros after the decimal point shift digits to smaller place values, making the number smaller.

How can I quickly tell which decimal is larger?

Compare digits from left to right after the decimal point. 0.250 has 2 in the tenths place, while 0.0250 has 0 in tenths and 2 in hundredths, so 0.250 is larger.

What's the easiest way to compare these decimals?

Convert to fractions with the same denominator or use place value. $0.250 = \frac{2500}{10000}$ and $0.0250 = \frac{250}{10000}$ , so clearly they're different!

Can I just remove all the zeros to compare?

No! You can only remove trailing zeros (at the end). Leading zeros after the decimal point are crucial for place value and cannot be removed.

How do I remember the difference between these types of zeros?

Think of it like money: $2.50 =$ 2.500 (trailing zeros don't matter), but $2.50 ≠$ 0.250 (leading zeros after decimal create different amounts).

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