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# 3.1 Rounding And Estimating

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Prentice Hall Sections 3.1 and 3.2 on Rounding and Estimating. Different types of estimating, plus estimating with multiplication and division.

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### 3.1 Rounding And Estimating

1. 1. Rounding And Estimating Section 3.1 By Ms. D-H
2. 2. Rounding Decimals <ul><li>You can round decimal numbers when you don’t need exact values. </li></ul><ul><li>Review: </li></ul>38. 4 1 0 .7772 7,098. 5 6 274.94 3 4 5. 0 25 9.8 5 1 Tenth, 38.4 Ones, 1 Tenths, 7,098.8 Thousandths, 274.943 Tenths, 5.0 Hundredths, 9.85
3. 3. Estimating Sums and Differences <ul><li>You can estimate an answer before you calculate, to make sure your answer is reasonable. </li></ul><ul><li>The symbol  means “is approximately equal to.” </li></ul><ul><li>One way to estimate is to round all of the numbers to the same place value. </li></ul>
4. 4. Estimating with Decimals <ul><li>Estimate to find whether each answer is reasonable. </li></ul>+130  +125.73 590  590.63 460  464.90 Estimate Calculation
5. 5. Try This: Estimate <ul><li>355.302 + 204.889 = </li></ul><ul><li>453.56 – 230.07 = </li></ul>About 560 About 220
6. 6. Front-End Estimating <ul><li>Gets you closer to the exact sum than estimating by rounding. </li></ul><ul><li>Add the front-end digits. (to the left of the decimal) </li></ul><ul><li>Round to estimate the sum of the remaining digits (to the right of the decimal) </li></ul><ul><li>Combine the two estimates. (add) </li></ul>
7. 7. Front-End Estimating <ul><li>Use Front-End Estimating: </li></ul>\$ 1 .10 \$ 1 .73 \$ 2 .71 \$ 4 . .10 .73 .71 . ? Estimate by Rounding. .10 .70 .70 1.50 Now add, \$4 + \$1.50 = \$5.50 The total cost is about \$5.50.
8. 8. Try This: Estimating using Front-End Estimation. <ul><li>6.75 + 2.2 + 9.58 = about… </li></ul><ul><li>\$1.04 + \$2.49 + \$7.40 = about… </li></ul>
9. 9. Clustering <ul><li>Use clustering to estimate the sum of several numbers that are close to one value. </li></ul><ul><li>Example: Phone Bills for 4 Months </li></ul>What dollar amount do the 4 bills cluster around? \$15.00 is our cluster value. 4 bills at,  \$15 means 4 • \$15 = \$60 is  the total cost. August: \$15.05 July: \$14.90 June: \$16.05 May: \$15.35
10. 10. Try This: Using Cluster Estimating <ul><li>\$4.50 + \$5.20 + \$5.55 = </li></ul><ul><li>26.7 + 26.2 + 24.52 + 25.25 + 23.9 = </li></ul>About \$15 About 125
11. 11. Estimating Decimal Products and Quotients Section 3.2
12. 12. Estimating Products <ul><li>You can use MENTAL MATH to estimate a product. </li></ul><ul><li>This is a good way to check your work! </li></ul><ul><li>Estimate! </li></ul>7.65 • 3.2 = ? 7.65 (by rounding) = 8 3.2 (by rounding) = 3 8 • 3  24 7.65 • 3.2  24
13. 13. Try This: Estimating Products <ul><li>4.72 • 1.8  </li></ul><ul><li>17.02 • 3.78  </li></ul><ul><li>8.25 • 19.8  </li></ul>
14. 14. Word Problem!!! <ul><li>Arlene bought 6 yards of fabric. The fabric cost \$6.75/yard. The sales clerk charged Arlene \$45.90 before tax. Did the clerk make a mistake? Explain. </li></ul>\$6.75  \$7 \$7 • 6 yards = \$42 Rounded to the nearest dollar. Multiplied the estimate. The sales clerk made a mistake. Since \$6.75 < \$7, the actual cost should be less than the estimate. The clerk should have charged Arlene less than \$42.00 before tax.
15. 15. Try This: Word Problem <ul><li>You buy 8 rolls of film for your camera (cause it is ancient). Each roll costs \$4.79. Estimate the cost of the film before tax. </li></ul>\$4.79 is rounded to \$5 \$5 • 8 rolls = \$40 \$4.79 • 8  \$40.00 Eight rolls of film at this price is about \$40.00 total.
16. 16. Estimating Quotients: Things to Remember <ul><li>Dividend </li></ul><ul><li>Divisor </li></ul><ul><li>Quotient </li></ul><ul><li>Compatible Numbers : numbers that are easy to divide mentally. </li></ul>24  8 = 3
17. 17. Estimating Quotients <ul><li>Round the divisor. </li></ul><ul><li>Round the dividend to a compatible number. </li></ul>38.9  1.79  11.95  2.1  82.52  4.25  1.79  2, 38.9  39, so 39  2 19 2.1  2, 11.95  12, so 12  2 6
18. 18. Assignment #15 <ul><li>Practice 3.1: Rounding and Estimating (All) </li></ul><ul><li>Practice 3.2: Estimating Decimal Products and Quotients (All) </li></ul><ul><li>50 problems total. </li></ul>