Compare Fractions and Decimals: Solving 2/20 ? 0.01

Q: Should I convert the fraction to decimal or the decimal to fraction?

Either way works! Converting fractions to decimals is often easier because you just divide. For $ \frac{2}{20} $, divide 2 ÷ 20 = 0.1, then compare 0.1 vs 0.01.

Q: Do I always need to simplify the fraction first?

Not always required, but it makes the math easier! $ \frac{2}{20} $ becomes the simpler $ \frac{1}{10} $, and 1 ÷ 10 = 0.1 is easier than 2 ÷ 20.

Q: How can I tell 0.1 is bigger than 0.01 without calculating?

Look at the place values! 0.1 has a 1 in the tenths place, while 0.01 has a 1 in the hundredths place. Tenths are bigger than hundredths, so 0.1 > 0.01.

Q: Can I use a number line to help compare?

Absolutely! Draw a number line and mark both values. 0.01 is very close to 0, while 0.1 is much further right, making it clearly larger.

Fraction-Decimal Comparison with Simplification

Choose the appropriate sign (?):

$\frac{2}{20}?0.01$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the appropriate sign

00:03 Reduce the fraction so the denominator equals 10

00:06 Factor 20 into 2 and 10

00:11 Reduce what we can

00:20 Now convert from fraction to decimal

00:23 Write the numerator as a whole number

00:28 When denominator equals 10, move the decimal point once to the left

00:31 Place the decimal instead of the fraction, and compare

00:34 Choose the correct sign

00:37 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 (?):

$\frac{2}{20}?0.01$

Step-by-step solution

To solve this problem, we'll compare the fraction $\frac{2}{20}$ to the decimal $0.01$ by converting both to the same form.

Step 1: Simplify the fraction $\frac{2}{20}$ .

$\frac{2}{20}$ simplifies to $\frac{1}{10}$ by dividing both the numerator and the denominator by 2.

Step 2: Convert the simplified fraction $\frac{1}{10}$ to a decimal.

Divide 1 by 10: $\frac{1}{10} = 0.1$ .

Step 3: Compare the decimal form of the fraction with $0.01$ .

We have $0.1$ and $0.01$ . Clearly, $0.1 > 0.01$ since $0.1$ is ten times larger than $0.01$ .

Therefore, the correct comparison sign for $\frac{2}{20} ? 0.01$ is $\gt$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Simplify fractions first, then convert to same form
Technique: Convert $\frac{2}{20}$ to $\frac{1}{10} = 0.1$
Check: Compare in decimal form: 0.1 > 0.01 because 0.1 is ten times larger ✓

Common Mistakes

Avoid these frequent errors

Comparing fractions and decimals without converting to same form
Don't try to compare $\frac{2}{20}$ and 0.01 directly = impossible to see which is bigger! Your brain can't easily compare different number forms. Always convert both numbers to the same form (both fractions OR both decimals) before comparing.

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

Should I convert the fraction to decimal or the decimal to fraction?

Either way works! Converting fractions to decimals is often easier because you just divide. For $\frac{2}{20}$ , divide 2 ÷ 20 = 0.1, then compare 0.1 vs 0.01.

Do I always need to simplify the fraction first?

Not always required, but it makes the math easier! $\frac{2}{20}$ becomes the simpler $\frac{1}{10}$ , and 1 ÷ 10 = 0.1 is easier than 2 ÷ 20.

How can I tell 0.1 is bigger than 0.01 without calculating?

Look at the place values! 0.1 has a 1 in the tenths place, while 0.01 has a 1 in the hundredths place. Tenths are bigger than hundredths, so 0.1 > 0.01.

What if the decimal has more digits, like 0.012?

Compare digit by digit from left to right! Start with tenths place: 0.1 has 1, 0.012 has 0. Since 1 > 0 in the tenths place, 0.1 > 0.012 automatically.

Can I use a number line to help compare?

Absolutely! Draw a number line and mark both values. 0.01 is very close to 0, while 0.1 is much further right, making it clearly larger.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Decimal Fractions - Basic questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime