University:
Purdue University
Course:
MA 15300 | College Algebra
Academic year:

2024
Views:

138

Pages:

5
Author:

Delphinixxc3

Question 1 How do you convert 3 1 8 3 8 1 into a decimal and percent? Answer 1 Explanation: Divide the numerator by the denominator and add the whole number to convert the mixed fraction into a decimal. 1 8 = 0.125 and 3 + 0.125 = 3.125 8 1 =0.125and3+0.125=3.125 As a decimal, 3 1 8 = 3.125 3 8 1 =3.125. Multiply by 100 to convert the decimal into a percentage: 3.125 × 100 = 312.50 % 3.125×100=312.50% Thus, 3 1 8 3 8 1 is 3.125 as a decimal and 312.50% as a percentage. Answer 2 To convert 3 1 8 3 8 1 to decimal form, first multiply the whole number by the denominator and add the numerator: 3 × 8 + 1 = 25 3×8+1=25 Now, divide: 25 8 = 3.125 8 25 =3.125 Thus, 3 1 8 = 3.125 3 8 1 =3.125. Question 2 What is 0.17 expressed as a fraction? Answer 1 0.17 = 17 100 0.17= 100 17 Multiply by 100: 0.17 × 100 = 17 0.17×100=17 So, 0.17 = 17 100 0.17= 100 17 , and it cannot be simplified further since 17 is prime. Answer 2 Explanation: If you multiply 0.17 by 100, you get 17. Thus, 17 100 100 17 is the final answer. Question 3 How do you convert 0. 27 ‾ 0. 27 (27 repeating) to a fraction? Answer 1 Solution: The fraction 0.27 can be written as an infinite sum: 0. 27 ‾ = 0.27 + 0.0027 + 0.000027 + … 0. 27 =0.27+0.0027+0.000027+… This is a geometric progression where 𝑎 1 = 0.27 a 1 =0.27 and 𝑟 = 0.01 r=0.01. The sum of this progression is: 𝑆 = 𝑎 1 1 − 𝑟 = 0.27 0.99 = 27 99 = 3 11 S= 1−r a 1 = 0.99 0.27 = 99 27 = 11 3 Thus, 0. 27 ‾ = 3 11 0. 27 = 11 3 . Answer 2 Explanation: The repeating decimal 0. 27 ‾ 0. 27 is converted by multiplying by 100, subtracting, and simplifying: 100 𝑥 = 27. 27 ‾ − 𝑥 = 0. 27 ‾ 100x=27. 27 −x=0. 27 Simplifying leads to: 27 99 = 3 11 99 27 = 11 3 Question 4 How do you write 0.09 as a fraction? Answer 1 A fraction with a denominator of 100 can be used to express the decimal. 0.09 = 9 100 0.09= 100 9 Answer 2 Explanation: Since every decimal can be expressed as a fraction with a denominator of 10 or a power of 10, 0.09 = 9 100 0.09= 100 9 Question 5 Express 0.85 as a fraction. Answer 1 The decimal 0.85 can be converted into the fraction 85 100 100 85 . Simplify the fraction: 85 100 = 17 20 100 85 = 20 17 Answer 2 We start by writing 0.85 = 85 100 0.85= 100 85 , then simplify by dividing by 5: 85 100 = 17 20 100 85 = 20 17 So, 0.85 = 17 20 0.85= 20 17 .