Jeremy incorrectly says that 7 1/8 is the same as 7.18. Convert 7 1/8 to a decimal correctly, then explain Jeremy’s likely error. a) 7 1/8 = 7.125; Jeremy likely misinterpreted the fraction as a decimal. b) 7 1/8 = 7.18; Jeremy likely made a rounding error. c) 7 1/8 = 7.875; Jeremy likely misread the fraction. d) 7 1/8 = 7.081; Jeremy likely used the wrong conversion.
The Correct Answer and Explanation is :
The correct conversion of (7 \frac{1}{8}) to a decimal is (7.125), so option a is correct.
Explanation of the Error
Jeremy’s confusion likely stems from a misunderstanding of how to interpret fractions and their conversion to decimals. Let’s break down the correct conversion of (7 \frac{1}{8}):
- Understanding the Fraction: The mixed number (7 \frac{1}{8}) consists of the whole number 7 and the fractional part (\frac{1}{8}). To convert it to a decimal, we first need to convert (\frac{1}{8}).
- Converting the Fraction: The fraction (\frac{1}{8}) is converted to a decimal by dividing 1 by 8. Performing this division:
[
1 \div 8 = 0.125
]
Thus, (\frac{1}{8} = 0.125). - Combining the Parts: Now, we combine the whole number part (7) and the decimal part (0.125):
[
7 + 0.125 = 7.125
]
Analyzing Jeremy’s Error
Jeremy claimed that (7 \frac{1}{8}) is the same as (7.18). This indicates that he may have misinterpreted the fraction or perhaps made an arbitrary guess.
- Misinterpretation of Fractions: Jeremy might have mistaken the numerator and denominator in his calculation, which can lead to confusion in the conversion process. Instead of performing the correct division, he may have inaccurately estimated or approximated the value of (\frac{1}{8}) to be closer to (0.18), leading to an incorrect decimal.
- Rounding Confusion: Additionally, it’s possible that he rounded (0.125) incorrectly, possibly thinking it should be rounded to two decimal places. However, (0.125) rounds to (0.13), which does not directly correlate with his answer.
This highlights the importance of understanding fraction conversions and accurately performing division, especially in educational contexts where precision is crucial.