This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Another one Jessy — let's solve it. Here are the solutions to the math problems: 1. Convert the following fractions into decimals. a) (5)/(8) Step 1: Divide the numerator by the denominator. (5)/(8) = 5 ÷ 8 = 0.625 The decimal is 0.625. b) (17)/(50) Step 1: Divide the numerator by the denominator. (17)/(50) = 17 ÷ 50 = 0.34 The decimal is 0.34. c) (9)/(20) Step 1: Divide the numerator by the denominator. (9)/(20) = 9 ÷ 20 = 0.45 The decimal is 0.45. 2. Express each of the following into decimals by first changing the denominator into a power of ten. a) (1)/(5) Step 1: Multiply the numerator and denominator by 2 to make the denominator 10. (1)/(5) = (1 × 2)/(5 × 2) = (2)/(10) Step 2: Convert the fraction to a decimal. (2)/(10) = 0.2 The decimal is 0.2. b) (3)/(4) Step 1: Multiply the numerator and denominator by 25 to make the denominator 100. (3)/(4) = (3 × 25)/(4 × 25) = (75)/(100) Step 2: Convert the fraction to a decimal. (75)/(100) = 0.75 The decimal is 0.75. c) (24)/(50) Step 1: Multiply the numerator and denominator by 2 to make the denominator 100. (24)/(50) = (24 × 2)/(50 × 2) = (48)/(100) Step 2: Convert the fraction to a decimal. (48)/(100) = 0.48 The decimal is 0.48. 3. Express each of the following as fractions. a) 0.6 Step 1: Write the decimal as a fraction with a denominator of 10. 0.6 = (6)/(10) Step 2: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2. (6 ÷ 2)/(10 ÷ 2) = (3)/(5) The fraction is (3)/(5). b) 2.27 Step 1: Write the decimal as a mixed number or an improper fraction. 2.27 = 2 + (27)/(100) = (200)/(100) + (27)/(100) = (227)/(100) The fraction is (227)/(100). c) 0.415 Step 1: Let x equal the repeating decimal. x = 0.4151515... Step 2: Multiply by 10 to move the non-repeating part to the left of the decimal. 10x = 4.151515... (1) Step 3: Multiply by 1000 (since two digits repeat after the non-repeating part) to move one full repeating block to the left of the decimal. 1000x = 415.151515... (2) Step 4: Subtract equation (1) from equation (2). 1000x - 10x &= 415.1515... - 4.1515... \\ 990x &= 411 Step 5: Solve for x. x = (411)/(990) Step 6: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 3. (411 ÷ 3)/(990 ÷ 3) = (137)/(330) The fraction is (137)/(330). 4. Express each of the following as decimals. a) (2)/(9) Step 1: Divide the numerator by the denominator. (2)/(9) = 2 ÷ 9 = 0.222... The decimal is 0.2. b) (1)/(6) Step 1: Divide the numerator by the denominator. (1)/(6) = 1 ÷ 6 = 0.1666... The decimal is 0.16. c) (3)/(7) Step 1: Divide the numerator by the denominator. (3)/(7) = 3 ÷ 7 = 0.428571428571... The decimal is 0.428571. 5. Round off the following numbers correct to 1 decimal place. a) 25.78 Step 1: Identify the first decimal place (7). Step 2: Look at the next digit (8). Since 8 is 5 or greater, round up the first decimal place. 25.78 ≈ 25.8 The rounded number is 25.8. b) 0.946 Step 1: Identify the first decimal place (9). Step 2: Look at the next digit (4). Since 4 is less than 5, keep the first decimal place as it is. 0.946 ≈ 0.9 The rounded number is 0.9. c) 199.994 Step 1: Identify the first decimal place (9). Step 2: Look at the next digit (9). Since 9 is 5 or greater, round up the first decimal place. Rounding 9 up results in a carry-over. 199.994 ≈ 200.0 The rounded number is 200.0. 6. Round off the following numbers to the nearest hundredths. a) 3.9623 Step 1: Identify the hundredths place (6). Step 2: Look at the next digit (2). Since 2 is less than 5, keep the hundredths place as it is. 3.9623 ≈ 3.96 The rounded number is 3.96. b) 19.9984 Step 1: Identify the hundredths place (9). Step 2: Look at the next digit (8). Since 8 is 5 or greater, round up the hundredths place. Rounding 9 up results in a carry-over to the tenths place, which also carries over to the units place. 19.9984 ≈ 20.00 The rounded number is 20.00. c) 23.5675 Step 1: Identify the hundredths place (6). Step 2: Look at the next digit (7). Since 7 is 5 or greater, round up the hundredths place. 23.5675 ≈ 23.57 The rounded number is 23.57. What's next?