Find the Missing Value: 0.55 < ? < 0.57 Decimal Inequality

Q: Why can't 0.55 or 0.57 be the answer?

The inequality uses , which means 'strictly less than.' The missing number must be greater than 0.55 and less than 0.57, but not equal to either boundary.

Q: How do I compare decimal numbers like this?

Compare digits from left to right! Since the ones and tenths places are the same (0.5_), look at the hundredths place: 5 \( 0.55 .

Q: Are there other numbers that would work?

Yes! Any decimal between 0.55 and 0.57 works, like 0.551, 0.56, 0.563, etc. But from the given choices, only 0.56 fits the range.

Q: What if the problem used ≤ instead of <?

If it were $ 0.55 ≤ ? ≤ 0.57 $, then the boundary values 0.55 and 0.57 would be included as possible answers. The ≤ symbol means 'less than or equal to.'

Q: How can I double-check my answer?

Substitute your answer into both parts: Is 0.55 Yes! Is 0.56 Yes! If both inequalities are true, your answer is correct.

Decimal Inequalities with Hundredths

Fill in the missing value (?):

$0.55 < ? < 0.57$

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Step-by-step video solution

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00:00 Complete the appropriate number

00:04 We will use the number line to find the possible numbers

00:16 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

Fill in the missing value (?):

$0.55 < ? < 0.57$

Step-by-step solution

The range of numbers in which the missing number can be is between 0.55 and 0.57.

The only number that is between those numbers is 56.

Therefore, the correct answer is (d).

Final Answer

$0.56$

Key Points to Remember

Essential concepts to master this topic

Range Rule: Find numbers strictly between the given decimal bounds
Technique: Check hundredths place: 0.56 falls between 0.55 and 0.57
Check: Verify 0.55 < 0.56 < 0.57 by comparing place values ✓

Common Mistakes

Avoid these frequent errors

Including the boundary values as possible answers
Don't think 0.55 or 0.57 can fill the blank = wrong inequality! The symbols < mean 'less than,' not 'less than or equal to.' Always find values strictly between the boundaries, excluding the endpoints.

Practice Quiz

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Which decimal number is greater?

FAQ

Everything you need to know about this question

Why can't 0.55 or 0.57 be the answer?

The inequality uses < symbols, which means 'strictly less than.' The missing number must be greater than 0.55 and less than 0.57, but not equal to either boundary.

How do I compare decimal numbers like this?

Compare digits from left to right! Since the ones and tenths places are the same (0.5_), look at the hundredths place: 5 < 6 < 7, so $0.55 < 0.56 < 0.57$ .

Are there other numbers that would work?

Yes! Any decimal between 0.55 and 0.57 works, like 0.551, 0.56, 0.563, etc. But from the given choices, only 0.56 fits the range.

What if the problem used ≤ instead of +

If it were $0.55 ≤ ? ≤ 0.57$ , then the boundary values 0.55 and 0.57 would be included as possible answers. The ≤ symbol means 'less than or equal to.'

How can I double-check my answer?

Substitute your answer into both parts: Is 0.55 < 0.56? Yes! Is 0.56 < 0.57? Yes! If both inequalities are true, your answer is correct.

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