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Solve a Simpler Problem and Look for a Pattern

It is not easy to simplify 8 23 with paper and pencil. You could simplify easier expressions, like 8 2 , 8 3 , and 8 4 , to see what number is in the ones place. You know that 8 23 is a large number to calculate. You need to find out what number is in the ones place. COURSE 2 LESSON 3-7.

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Solve a Simpler Problem and Look for a Pattern

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  1. It is not easy to simplify 823 with paper and pencil. You could simplify easier expressions, like 82, 83, and 84, to see what number is in the ones place. You know that 823 is a large number to calculate. You need to find out what number is in the ones place. COURSE 2 LESSON 3-7 Solve a Simpler Problem and Look for a Pattern When you simplify 823, what is the ones digit? 3-7

  2. Power Value 81 8 82 64 83 512 84 4,096 85 32,768 86 262,144 87 2,097,152 88 16,777,216 89 134,217,728 810 1,073,741,824 COURSE 2 LESSON 3-7 Solve a Simpler Problem and Look for a Pattern (continued) Step 1:Solve a Simpler Problem Find the values of the first 10 powers of 8. Refer to the table at the right. Notice that the ones digits in the value column repeat in the pattern 8, 4, 2, 6. 3-7

  3. Ones Place Exponent of 8 8 1, 5, 9 4 2, 6, 10 2 3, 7 6 4, 8 If the exponent is divisible by 4, then the ones digit is 6. Since 20 is divisible by 4, you can start there: Exponent: 20 21 22 23 Ones digit: 6 8 4 2 COURSE 2 LESSON 3-7 Solve a Simpler Problem and Look for a Pattern (continued) Step 2:Look for a Pattern Organize the information to see whether there is a connection between the ones digits and the exponents. Refer to the table at the right. The number in the ones place of 823 is 2. 3-7

  4. COURSE 2 LESSON 3-7 Solve a Simpler Problem and Look for a Pattern (continued) Look for a pattern in another row of the exponent table that might also work. When the exponent of 8 is 2, 6, or 10, the ones digit is 4. The numbers 2, 6, and 10 are divisible by 2, but not by 4. Since 22 is divisible by 2 but not by 4, the ones digit of 822 is 4. Exponent: 22 23 Ones digit: 4 2 3-7

  5. COURSE 2 LESSON 3-7 Solve a Simpler Problem and Look for a Pattern 1. What is the eighth number in the pattern: 5, 25, 125, 625, 3,125, 15,625, . . .? 2. A jump-rope manufacturer has invited 128 teams to participate in a rope-jumping contest. Teams are paired, and any team that loses one match is eliminated from the contest. How many matches are needed to determine the winner? 390,625 127 3-7

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