Compare Mixed Numbers: Is 2.07 Equal to, Less Than, or Greater Than 2.7?

Q: How do I know which decimal is bigger?

Start from the left and compare digit by digit. In 2.07 vs 2.7, both have 2 ones, but 2.07 has 0 tenths while 2.7 has 7 tenths, so 2.7 is larger.

Q: Can I compare without converting to decimals?

Yes, but it's trickier! You'd need to convert 2.7 to a mixed number like $ 2\frac{70}{100} $, then compare $ \frac{7}{100} $ vs $ \frac{70}{100} $.

Q: What if the decimals have different numbers of digits?

Add zeros to make them the same length! 2.7 becomes 2.70, making it easier to see that 2.07

Q: How can I remember which symbol means what?

Think of the symbol as a hungry mouth that always wants to eat the bigger number! So

Decimal Comparison with Mixed Numbers

Choose the appropriate sign (?):

$2\frac{7}{100}?2.7$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the appropriate sign

00:03 Convert decimal fraction to complex fraction

00:07 Break down into whole number and remainder

00:10 Convert the remainder to a fraction

00:13 Place the digits in the numerator

00:17 Move the decimal point right until we get a whole number

00:20 We moved once, so the denominator will be equal to 10

00:23 Expand the fraction to match the common denominator 100

00:27 Make sure to multiply both numerator and denominator

00:32 Calculate the multiplications

00:37 Combine into a complex fraction

00:42 Place the fraction in place of the decimal fraction, and compare

00:49 Choose the appropriate sign

00:52 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 (?):

$2\frac{7}{100}?2.7$

Step-by-step solution

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

Step 1: Convert $2\frac{7}{100}$ to a decimal.
Step 2: Compare the resultant decimal with $2.7$ .

Now, let's work through each step:

Step 1: Convert the mixed number $2\frac{7}{100}$ into a decimal.

The whole number part is $2$ , and the fractional part $\frac{7}{100}$ as a decimal is $0.07$ . Therefore, the mixed number:

$2\frac{7}{100} = 2 + 0.07 = 2.07$

Step 2: Compare $2.07$ to $2.7$ .

Since $2.07$ is less than $2.7$ , we conclude that:

$2\frac{7}{100} < 2.7$

Therefore, the appropriate sign to choose is $<$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Conversion: Transform mixed numbers to decimals for easier comparison
Technique: $2\frac{7}{100} = 2 + 0.07 = 2.07$
Check: Compare place values: 2.07 has 0 tenths, 2.7 has 7 tenths ✓

Common Mistakes

Avoid these frequent errors

Ignoring place value positions when comparing decimals
Don't think 2.07 > 2.7 because 07 > 7 = wrong comparison! This ignores that 0.07 means 7 hundredths while 2.7 means 7 tenths. Always align decimal places and compare digit by digit from left to right.

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 do I need to convert the mixed number to a decimal?

Converting to decimals makes comparison much easier! When both numbers are in the same format, you can directly compare their place values without confusion.

How do I know which decimal is bigger?

Start from the left and compare digit by digit. In 2.07 vs 2.7, both have 2 ones, but 2.07 has 0 tenths while 2.7 has 7 tenths, so 2.7 is larger.

Can I compare without converting to decimals?

Yes, but it's trickier! You'd need to convert 2.7 to a mixed number like $2\frac{70}{100}$ , then compare $\frac{7}{100}$ vs $\frac{70}{100}$ .

What if the decimals have different numbers of digits?

Add zeros to make them the same length! 2.7 becomes 2.70, making it easier to see that 2.07 < 2.70 since 07 < 70 in the hundredths place.

How can I remember which symbol means what?

Think of the symbol as a hungry mouth that always wants to eat the bigger number! So < means 'less than' because the mouth opens toward the larger number.

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