Compare Fractions and Decimals: 25/10 and 0.25 Relationship

Q: Why don't I just compare 25 and 25 since they're the same number?

The position of numbers matters! In $ \frac{25}{10} $, the 25 is in the ones and tenths places (2.5), while in 0.25, it's in the tenths and hundredths places. Same digits, different values!

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

Look at the whole number part first. Since 2.5 has 2 in the ones place and 0.25 has 0, then 2.5 is automatically bigger. No need to compare the decimal parts!

Q: What's the easiest way to convert simple fractions like 25/10?

For fractions with denominators of 10, 100, 1000, just move the decimal point! $ \frac{25}{10} $ means move the decimal in 25.0 one place left to get 2.5.

Fraction to Decimal Conversion with Mixed Values

Choose the appropriate sign (?):

$\frac{25}{10}?0.25$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the correct sign

00:03 Convert decimal to simple fraction

00:08 Place the digits in the numerator

00:12 Move the decimal point until we get a whole number to find the denominator

00:15 We moved the decimal point 2 places right, so the denominator equals 100

00:20 Place the fraction instead of the decimal fraction

00:24 Now expand the second fraction to the common denominator 100

00:29 Make sure to multiply both numerator and denominator

00:44 Place this fraction and compare

00:49 Choose the appropriate sign

00:53 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 appropriate sign (?):

$\frac{25}{10}?0.25$

Step-by-step solution

To compare the given values, we first convert the fraction $\frac{25}{10}$ into a decimal form:

Step 1: Simplify $\frac{25}{10}$ .

Divide 25 by 10:

$\frac{25}{10} = 2.5$ .

Step 2: Compare 2.5 and 0.25.

The decimal $2.5$ is clearly greater than $0.25$ .

Thus, the correct comparison sign between the values is greater than.

Therefore, we write:

$\frac{25}{10} > 0.25$ .

Thus, the correct choice is >.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: Divide numerator by denominator to get decimal form
Technique: $\frac{25}{10} = 25 ÷ 10 = 2.5$
Check: Compare decimal values: 2.5 > 0.25 confirms the relationship ✓

Common Mistakes

Avoid these frequent errors

Confusing decimal place values when comparing
Don't assume 0.25 is bigger than 2.5 because 25 > 2! This ignores decimal place value and gives completely wrong comparisons. Always align decimal points mentally: 2.50 versus 0.25 makes the size difference clear.

Practice Quiz

Test your knowledge with interactive questions

Write the following fraction as a decimal:

$\frac{5}{100}=$

FAQ

Everything you need to know about this question

Why don't I just compare 25 and 25 since they're the same number?

The position of numbers matters! In $\frac{25}{10}$ , the 25 is in the ones and tenths places (2.5), while in 0.25, it's in the tenths and hundredths places. Same digits, different values!

How can I quickly tell which decimal is bigger?

Look at the whole number part first. Since 2.5 has 2 in the ones place and 0.25 has 0, then 2.5 is automatically bigger. No need to compare the decimal parts!

What if both numbers were less than 1?

Then compare digit by digit from left to right after the decimal point. For example: 0.7 > 0.25 because 7 tenths is greater than 2 tenths.

Should I always convert fractions to decimals for comparison?

Not always! You can also convert decimals to fractions: 0.25 = $\frac{25}{100} = \frac{1}{4}$ , then compare $\frac{25}{10}$ and $\frac{1}{4}$ using common denominators.

What's the easiest way to convert simple fractions like 25/10?

For fractions with denominators of 10, 100, 1000, just move the decimal point! $\frac{25}{10}$ means move the decimal in 25.0 one place left to get 2.5.

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