Compare 7/100 and 0.7: Finding the Correct Mathematical Symbol

Q: Why can't I just look at the numerators since they're both 7?

Because the denominators are different! $ \frac{7}{100} $ means 7 out of 100 parts, while $ \frac{7}{10} $ means 7 out of 10 parts. Think of it like pizza slices - 7 slices from a pizza cut into 100 pieces vs 7 slices from a pizza cut into 10 pieces!

Q: Is there an easier way than cross-multiplication?

Yes! Convert both to decimals: $ \frac{7}{100} = 0.07 $ and $ 0.7 $. Now it's easy to see that 0.07 .

Q: How do I convert fractions to decimals quickly?

Divide the numerator by the denominator! For $ \frac{7}{100} $, think: 7 ÷ 100 = 0.07. The denominator 100 tells you the decimal has 2 zeros, so 7 becomes 0.07.

Q: What if I get confused about which symbol to use?

Remember: the smaller number gets the smaller end of the symbol! Since 0.07 \( \frac{7}{100} . The symbol points toward the smaller value.

Q: Can I make both fractions have the same denominator instead?

Absolutely! Convert $ \frac{7}{10} $ to $ \frac{70}{100} $ by multiplying top and bottom by 10. Now compare $ \frac{7}{100} $ vs $ \frac{70}{100} $ - clearly 7 !

Fraction-Decimal Comparisons with Different Denominators

Choose the missing sign (?):

$\frac{7}{100}?0.7$

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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 a decimal fraction to a simple fraction

00:07 Place the digits in the numerator

00:10 Move the decimal point right until the number is whole and not decimal

00:13 We moved once, so the denominator will equal 10

00:19 Now we'll expand the fraction to the common denominator

00:22 Make sure to multiply both numerator and denominator

00:31 Now we'll place the fraction instead of the decimal fraction

00:36 Adjust the sign according to the numerators

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 (?):

$\frac{7}{100}?0.7$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Convert the decimal $0.7$ into a fraction for easy comparison.
Step 2: Compare the fractions $\frac{7}{100}$ and $\frac{7}{10}$ using cross-multiplication.

Now, let's work through each step:
Step 1: Convert $0.7$ to a fraction. Since $0.7 = \frac{7}{10}$ , we convert it to this fraction.
Step 2: Compare $\frac{7}{100}$ and $\frac{7}{10}$ using cross-multiplication.
Calculate $7 \times 10 = 70$ and $7 \times 100 = 700$ .

Since $70 < 700$ , it follows that $\frac{7}{100} < \frac{7}{10}$ .

Therefore, the solution to the problem is $<$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Convert to same form before comparing fractions and decimals
Technique: Convert $0.7 = \frac{7}{10}$ , then cross-multiply: 7×10 vs 7×100
Check: Verify $\frac{7}{100} = 0.07 < 0.7$ makes sense ✓

Common Mistakes

Avoid these frequent errors

Comparing numerators only when denominators differ
Don't just compare 7 and 7 in $\frac{7}{100}$ vs $\frac{7}{10}$ = wrong conclusion they're equal! The denominators are different (100 vs 10), so you need different amounts. Always convert to same denominator or use cross-multiplication.

Practice Quiz

Test your knowledge with interactive questions

Convert into fraction form:

$$ 0.38= $$

FAQ

Everything you need to know about this question

Why can't I just look at the numerators since they're both 7?

Because the denominators are different! $\frac{7}{100}$ means 7 out of 100 parts, while $\frac{7}{10}$ means 7 out of 10 parts. Think of it like pizza slices - 7 slices from a pizza cut into 100 pieces vs 7 slices from a pizza cut into 10 pieces!

Is there an easier way than cross-multiplication?

Yes! Convert both to decimals: $\frac{7}{100} = 0.07$ and $0.7$ . Now it's easy to see that 0.07 < 0.7.

How do I convert fractions to decimals quickly?

Divide the numerator by the denominator! For $\frac{7}{100}$ , think: 7 ÷ 100 = 0.07. The denominator 100 tells you the decimal has 2 zeros, so 7 becomes 0.07.

What if I get confused about which symbol to use?

Remember: the smaller number gets the smaller end of the symbol! Since 0.07 < 0.7, we write $\frac{7}{100} < 0.7$ . The symbol points toward the smaller value.

Can I make both fractions have the same denominator instead?

Absolutely! Convert $\frac{7}{10}$ to $\frac{70}{100}$ by multiplying top and bottom by 10. Now compare $\frac{7}{100}$ vs $\frac{70}{100}$ - clearly 7 < 70!

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