Which of the following points on the number line best represents 5/8 ?
1) 0.5
2) 0.625
3) 0.75
4) 0.875
The Correct Answer and Explanation is:
To determine which of the given points on the number line best represents ( \frac{5}{8} ), we first need to convert the fraction into a decimal format. The fraction ( \frac{5}{8} ) can be computed by dividing 5 by 8.
Decimal Conversion
- Division:
- To divide 5 by 8, we can perform long division.
- 8 goes into 5 zero times. We then append a decimal point and a zero, making it 50.
- 8 goes into 50 six times (since ( 8 \times 6 = 48 )).
- Subtracting 48 from 50 leaves us with 2.
- Bringing down another zero makes it 20.
- 8 goes into 20 two times (since ( 8 \times 2 = 16 )).
- Subtracting 16 from 20 leaves us with 4.
- Bringing down another zero makes it 40.
- 8 goes into 40 five times (since ( 8 \times 5 = 40 )).
- Subtracting gives us 0.
Putting all this together, we find that:
[
\frac{5}{8} = 0.625
]
Analysis of Options
Now, we compare this decimal value ( 0.625 ) with the given options:
- 0.5: This is equivalent to ( \frac{1}{2} ) and is less than ( \frac{5}{8} ).
- 0.625: This is exactly equal to ( \frac{5}{8} ).
- 0.75: This is equivalent to ( \frac{3}{4} ) and is greater than ( \frac{5}{8} ).
- 0.875: This is equivalent to ( \frac{7}{8} ) and is also greater than ( \frac{5}{8} ).
Conclusion
From this analysis, we conclude that the point that best represents ( \frac{5}{8} ) on the number line is option 2) 0.625.
This shows the importance of converting fractions to decimals for easier comparisons and visual representations on a number line. Understanding the relationship between fractions and their decimal equivalents is a fundamental skill in mathematics that aids in various applications, including measurement, financial calculations, and data interpretation. Thus, recognizing that ( \frac{5}{8} ) equals ( 0.625 ) helps ensure accurate representation on a number line and strengthens numerical literacy.