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Understanding Decimals and Circle Circumference Calculation

Learn how to multiply decimals step by step, estimate the results, and compute decimals by powers of 10. Discover the formula for calculating the circumference of a circle using radius or diameter with detailed examples and approximations.

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Understanding Decimals and Circle Circumference Calculation

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  1. Multiplying Decimals and Circumference of a Circle 5.3

  2. Multiplying Decimals 21 7 3  1000 10 100 Multiplying decimals is similar to multiplying whole numbers. The difference is that we place a decimal point in the product. 0.7  0.03 = = = 0.021 1 decimal place 2 decimal places 3 decimal places

  3. Multiplying Decimals Step 1: Multiply the decimals as though they were whole numbers. Step 2: The decimal point in the product is placed so the number of decimal places in the product is equal to the sumof the number of decimal places in the factors.

  4. Estimating when Multiplying Decimals Multiply 32.3  1.9. Exact Estimate rounds to rounds to This is a reasonable answer.

  5. Multiplying Decimals by Powers of 10 There are some patterns that occur when we multiply a number by a power of ten, such as 10, 100, 1000, 10,000, and so on.

  6. Multiplying Decimals by Powers of 10 Decimal point moved 1 place to the right. 76.543  10 = 765.43 76.543  100 = 7654.3 76.543  100,000 = 7,654,300 1 zero Decimal point moved 2 places to the right. 2 zeros Decimal point moved 5 places to the right. 5 zeros The decimal point is moved the same number of places as there are zeros in the power of 10.

  7. Multiplying Decimals by Powers of 10 Move the decimal point to theright thesame number of places as there arezerosin the power of 10. Multiply: 3.4305  100 Since there are two zeros in 100, move the decimal place two places to the right. 3.4305  100 = 3.4305 = 343.05

  8. Multiplying Decimals by Powers of 10 Move the decimal point to theleftthesame number of places as there aredecimal placesin the power of 10. Multiply: 8.57  0.01 Since there are two decimal places in 0.01, move the decimal place two places to the left. 8.57  0.01 = 008.57 = 0.0857 Notice that zeros had to be inserted.

  9. The Circumference of a Circle The distance around a polygon is called itsperimeter. The distance around a circle is called thecircumference. This distance depends on theradiusor thediameter of the circle.

  10. The Circumference of a Circle r d Circumference= 2·p·radius or Circumference = p·diameter C= 2prorC= pd

  11. 22 7 p The symbolpis the Greek letter pi, pronounced “pie.” It is a constant between 3 and 4. A decimal approximation forpis 3.14. A fraction approximation forpis.

  12. The Circumference of a Circle Find the circumference of a circle whose radius is 4 inches. 4 inches C = 2pr = 2p ·4 = 8pinches 8p inches is the exact circumference of this circle. If we replace  with the approximation 3.14, C = 8  8(3.14) = 25.12 inches. 25.12 inches is the approximate circumference of the circle.

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