Select the model that represents the decimal 1.07. Then find percent and fraction equivalents for 1.07. The percent equivalent of 1.07 is
The Correct Answer and Explanation is:
The decimal 1.07 can be represented as:
- Fraction Equivalent:
To convert 1.07 into a fraction, first separate the whole number and the decimal: 1.07=1+0.071.07 = 1 + 0.071.07=1+0.07 Now, express 0.07 as a fraction: 0.07=71000.07 = \frac{7}{100}0.07=1007 Therefore: 1.07=1+7100=100100+7100=1071001.07 = 1 + \frac{7}{100} = \frac{100}{100} + \frac{7}{100} = \frac{107}{100}1.07=1+1007=100100+1007=100107 So, the fraction equivalent of 1.07 is 107/100. - Percent Equivalent:
To convert 1.07 into a percentage, multiply the decimal by 100: 1.07×100=107%1.07 \times 100 = 107\%1.07×100=107% Therefore, the percent equivalent of 1.07 is 107%.
Explanation:
- The fraction equivalent of a decimal is found by expressing the decimal part as a fraction over a power of 10 (depending on how many decimal places there are). In this case, 0.07 is represented as 7/100, and the whole number 1 is represented as 100/100, leading to the fraction 107/100.
- The percent equivalent is simply obtained by multiplying the decimal by 100, because percent means “per hundred.” Thus, 1.07 becomes 107%, which indicates 107 parts out of 100 or a value slightly greater than 1.
Both these conversions (to a fraction and percentage) are fundamental methods of expressing and understanding the relationship between decimal, fractional, and percent forms of a number.
