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.
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here are the solutions to your problems. 9. B.E.S.T. TEST PREP Select all the true statements. Step 1: Evaluate each statement. A) 0.029 is (1)/(10) of 2.90. 2.90 ÷ 10 = 0.29. Since 0.029 ≠ 0.29, this statement is false. B) 0.029 is (1)/(100) of 2.90. 2.90 ÷ 100 = 0.029. This statement is true. C) 2.90 is 10 times as great as 0.029. 0.029 × 10 = 0.29. Since 2.90 ≠ 0.29, this statement is false. D) 0.029 is 100 times as great as 0.029. 0.029 × 100 = 2.9. Since 0.029 ≠ 2.9, this statement is false. E) 2.90 is 100 times as great as 0.029. 0.029 × 100 = 2.9. This statement is true. The true statements are B and E. 10. Adapt a Procedure Complete each statement. Explain your procedure. Statement 1: 2780 is 1,000 times as great as 2.78. Procedure:* To find a number 1,000 times as great, multiply 2.78 by 1,000. This shifts the decimal point three places to the right. 2.78 × 1,000 = 2780 Statement 2: 27800 is 10,000 times as great as 2.78. Procedure:* To find a number 10,000 times as great, multiply 2.78 by 10,000. This shifts the decimal point four places to the right. 2.78 × 10,000 = 27800 Statement 3: 0.027 is (1)/(1,000) of 27. Procedure:* To find a number that is (1)/(1,000) of 27, divide 27 by 1,000. This shifts the decimal point three places to the left. 27 ÷ 1,000 = 0.027 Statement 4: 0.0027 is (1)/(10,000) of 27. Procedure:* To find a number that is (1)/(10,000) of 27, divide 27 by 10,000. This shifts the decimal point four places to the left. 27 ÷ 10,000 = 0.0027 11. Model Real Life Two baseball players have batting averages of 0.362 and 0.325. How do the values of the 2s in the batting averages compare? Step 1: Identify the value of '2' in 0.362. The '2' is in the thousandths place, so its value is 0.002. Step 2: Identify the value of '2' in 0.325. The '2' is in the hundredths place, so its value is 0.02. Step 3: Compare the two values. 0.02 ÷ 0.002 = 10 The value of the '2' in 0.325 (0.02) is 10 times as great as the value of the '2' in 0.362 (0.002). 12. Model Real Life How do the values of the 5s in the puffin weights compare? Step 1: Identify the value of '5' in the Atlantic puffin's weight (17.5 ounces). The '5' is in the tenths place, so its value is 0.5. Step 2: Identify the value of '5' in the Tufted puffin's weight (25.47 ounces). The '5' is in the ones place, so its value is 5. Step 3: Compare the two values. 5 ÷ 0.5 = 10 The value of the '5' in the Tufted puffin's weight (5) is 10 times as great as the value of the '5' in the Atlantic puffin's weight (0.5). 13. How do the values of the 7s in the puffin weights compare? Step 1: Identify the value of '7' in the Atlantic puffin's weight (17.5 ounces). The '7' is in the ones place, so its value is 7. Step 2: Identify the value of '7' in the Tufted puffin's weight (25.47 ounces). The '7' is in the hundredths place, so its value is 0.07. Step 3: Compare the two values. 7 ÷ 0.07 = 100 The value of the '7' in the Atlantic puffin's weight (7) is 100 times as great as the value of the '7' in the Tufted puffin's weight (0.07). Review & Refresh 14. Find the factor pairs for the number 9. Step 1: List pairs of numbers that multiply to 9. 1 × 9 = 9 3 × 3 = 9 The factor pairs for 9 are (1, 9), (3, 3). 15. Find the factor pairs for the number 24. Step 1: List pairs of numbers that multiply to 24. 1 × 24 = 24 2 × 12 = 24 3 × 8 = 24 4 × 6 = 24 The factor pairs for 24 are (1, 24), (2, 12), (3, 8), (4, 6). 16. Find the factor pairs for the number 15. Step 1: List pairs of numbers that multiply to 15. 1 × 15 = 15 3 × 5 = 15 The factor pairs for 15 are (1, 15), (3, 5). Drop the next question!