String A is 0.6 meter long. String B is 0.21 meter long. Vijay writes a comparison for 0.6 and 0.21. Vijay says that String B is longer than String A because 21 is greater than 6.... String A is 0.6 meter long. String B is 0.21 meter long. Vijay writes a comparison for 0.6 and 0.21. Vijay says that String B is longer than String A because 21 is greater than 6. Explain Vijay's mistake. Write your answer and your work or explanation in the space below.
Understand the Problem
The question asks to explain why Vijay's statement about the lengths of String A and String B is incorrect, focusing on the comparison between 0.6 and 0.21. It highlights a misunderstanding in Vijay's logic regarding numerical comparison.
Answer
Vijay's mistake is that $0.6$ is greater than $0.21$, as $0.60 > 0.21$.
Answer for screen readers
Vijay's statement is incorrect because $0.6$ (or $0.60$) is greater than $0.21$.
Steps to Solve
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Understanding the Comparison Vijay is comparing the numbers 0.6 and 0.21, believing that 21 (from 0.21) is greater than 6 (from 0.6). However, this is incorrect as he's comparing digits rather than the whole numbers.
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Correct Comparison of the Numbers In decimal numbers, $0.6$ means six tenths, which can be expressed as $0.60$ to make the comparison clearer. So we can compare $0.60$ and $0.21$ directly.
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Evaluating the Comparison When comparing $0.60$ and $0.21$, we analyze each the tenths and hundredths place:
- In terms of tenths, $0.60$ has 6 tenths and $0.21$ has 2 tenths.
- Therefore, $0.60 > 0.21$.
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Conclusion about Vijay's Mistake Vijay's mistake arises from taking the digits of the decimal numbers (21 and 6) out of context and not understanding that $0.6$ is actually greater than $0.21$.
Vijay's statement is incorrect because $0.6$ (or $0.60$) is greater than $0.21$.
More Information
In decimal notation, numbers are broken down into tenths, hundredths, and so on. Therefore, understanding the value of each digit's position is crucial in numerical comparisons.
Tips
Common mistakes include:
- Misunderstanding decimal places and comparing digits rather than numerical values.
- Forgetting that leading zeros in decimals do not affect the number’s value (e.g., treating $0.60$ and $0.6$ equally).
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