Compare 0.8 and 8/100: Choosing the Correct Mathematical Symbol

Q: How do I convert fractions with 100 in the denominator?

When the denominator is 100, you're working with hundredths! Simply take the numerator and move the decimal point two places to the left. For example: $ \frac{8}{100} = 0.08 $, $ \frac{25}{100} = 0.25 $.

Q: Can I just compare 0.8 and 8 directly?

No! You must convert both numbers to the same format first. Either convert both to decimals ($ 0.8 $ vs $ 0.08 $) or both to fractions ($ \frac{80}{100} $ vs $ \frac{8}{100} $). Never compare mixed formats!

Q: Why does the explanation show 008. instead of just 8?

This is a helpful visualization trick! Writing $ 008. $ shows where the decimal point starts, then moving it two places left for division by 100 gives $ 0.08 $. It helps you see the place value movement clearly.

Decimal Comparison with Fraction Conversion

Choose the missing sign (?):

$0.8?\frac{8}{100}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the appropriate sign

00:04 Convert fraction to decimal number

00:15 Dividing by hundred equals moving the decimal point 2 places left

00:33 Now let's compare the digits

00:36 The digit 8 is greater than 0, so the number is larger

00:39 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 missing sign (?):

$0.8?\frac{8}{100}$

Step-by-step solution

First, let's convert the simple fraction into a decimal fraction.

We'll write the number 8 with two zeros in front of it and then add the decimal point:

$\frac{8}{100}=008.$

Since the simple fraction is divided by 100, we'll move the decimal point two places to the left:

$008.=0.08$

Let's finally compare our two decimal numbers, focusing on the number after the decimal point:

$0.80 > 0.08$

Final Answer

$>$

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: Convert fractions to decimals by dividing numerator by denominator
Technique: $\frac{8}{100} = 8 \div 100 = 0.08$ by moving decimal two places left
Check: Compare place values: 0.8 has 8 tenths, 0.08 has 8 hundredths ✓

Common Mistakes

Avoid these frequent errors

Confusing place values when comparing decimals
Don't think 0.8 = 0.08 because both have the digit 8 = wrong comparison! The 8 is in different place values (tenths vs hundredths). Always identify which decimal place each digit occupies before comparing.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Why is 0.8 bigger than 8/100 if 8 is the same in both?

Great observation! The digit 8 appears in both numbers, but it's in different place values. In 0.8, the 8 is in the tenths place (worth 8/10). In 8/100 = 0.08, the 8 is in the hundredths place (worth 8/100). Since 8/10 > 8/100, we have 0.8 > 0.08.

How do I convert fractions with 100 in the denominator?

When the denominator is 100, you're working with hundredths! Simply take the numerator and move the decimal point two places to the left. For example: $\frac{8}{100} = 0.08$ , $\frac{25}{100} = 0.25$ .

Can I just compare 0.8 and 8 directly?

No! You must convert both numbers to the same format first. Either convert both to decimals ( $0.8$ vs $0.08$ ) or both to fractions ( $\frac{80}{100}$ vs $\frac{8}{100}$ ). Never compare mixed formats!

What if I get confused about which decimal is bigger?

Line them up by decimal points and compare digit by digit from left to right! $0.80$ vs $0.08$ : First digit after decimal is 8 vs 0, so $0.80 > 0.08$ . You can also think: 8 dimes vs 8 pennies!

Why does the explanation show 008. instead of just 8?

This is a helpful visualization trick! Writing $008.$ shows where the decimal point starts, then moving it two places left for division by 100 gives $0.08$ . It helps you see the place value movement clearly.

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