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Decimal Operations: Reading, Rounding, Adding, Subtracting, Multiplying, and Dividing

Learn how to read and write decimals, round decimals, and perform operations like addition, subtraction, multiplication, and division with decimals.

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Decimal Operations: Reading, Rounding, Adding, Subtracting, Multiplying, and Dividing

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  1. Instructor: Dr.Gehan Shanmuganathan

  2. Learning Outcomes 3-1 • Read and write decimals. • Round decimals.

  3. Our money system, based on the dollar, uses the decimal system. Moving one place from right to left increases the value ten times. Moving one place from left to right, causes the value of the number to become ten times smaller. Read and write decimals 3-1-1 Section 3-1 Decimal and Place-Value System

  4. It is one part of a 10-part whole. 0.1 is read “one tenth.” How much is .01? HOW TO: Section 3-1 Decimal and Place-Value System If this chart represented a dollar,the white segment would beequal to $0.10 (ten cents)

  5. It separates the whole number partfrom the decimal part, as the number extends fromleft to right. 26.8 is read twenty-six and eight tenths. Or 26 point8. The decimal point HOW TO: Section 3-1 Decimal and Place-Value System

  6. The first place to the right of the decimal point is tenths—0.1 Second place is hundredths—0.01 Third place is thousandths—0.001 Fourth place is ten-thousandths.0.0001 Place value names HOW TO: Section 3-1 Decimal and Place-Value System …and so on

  7. Read the whole number part first, saying “and”to indicate the beginning of the decimal part of the number. Read or write a decimal HOW TO: Section 3-1 Decimal and Place-Value System 4.15— Four and fifteen hundredths 9.067—Nine and sixty-seven thousandths. 5.5—Five and five tenths.

  8. When reading numbers that represent money amounts, read whole numbers as dollars. Decimal amounts are read as “cents.” Because 1 cent is one hundredth of a dollar, the words cent andhundredth have the same meaning. TIP: Reading decimals as money amounts HOW TO: Section 3-1 Decimal and Place-Value System $46.57 is read “forty-six dollars and fifty-seven cents.”

  9. Read and write decimals HOW TO: Section 3-1 Decimal and Place-Value System • Find the digit in the specified place, and look at the next digit to the right. • If this digit is less than 5, eliminate it, and all digitsto its right. • If this digit is 5 or more, add 1 to the digit in the specified place, and eliminate all digits to its right.

  10. Round to the nearest tenth Examples… Section 3-1 Decimal and Place-Value System 12.5 31,343.4 346.3 12.456 31,343.387 346.2778

  11. Learning Outcomes 3-2 • Add and subtract decimals. • Multiply decimals. • Divide decimals.

  12. Add and subtract decimals 3-2-1 Section 3-2 Operations with Decimals • Add or subtract as though the numbers are whole numbers. • Place the decimal point in the sum or differenceto align with the decimal point in the respective operation.

  13. Add and subtract decimals 3-2-1 Section 3-2 Operations with Decimals Attach extra zeros to the right end of each number so each number has the same quantity of digits.

  14. Add & Subtract Examples… Section 3-2 Operations with Decimals 6.485 + 1.4 + 0.8 + 11.999 = 10.008 – 7.6 = 0.976 – 0.04217 = 20.684 2.408 0.93383

  15. Multiply the decimal numbers as though theyare whole numbers. Count the digits in the decimal parts of both decimal numbers. Place the decimal point in the product so that there are as many digits in its decimal part as there are digits you counted in the previous step. If necessary, attach zeros to the left end of the product to place the decimal point accurately. Multiply decimals 3-2-2 Section 3-2 Operations with Decimals

  16. Example… HOW TO: Section 3-2 Operations with Decimals 3.45 x 4.082 = How many places are there tothe right of the decimal point? Five—so the product will have fiveplaces to the right of the decimal. 3.45 x 4.082 = 14.08290 The last zero can be droppedand the answer would be 14.0829.

  17. Multiplication Examples… Section 3-2 Operations with Decimals 1.7 x 0.08 = 4.67 x 5.004 = 0.01 x 1.001= 0.136 23.36868 0.01001

  18. Place a decimal point for the quotient directly above the decimal point in the dividend. Divide as though the decimal points are whole numbers. Divide decimals 3-2-3 Section 3-2 Operations with Decimals

  19. Division Examples… Section 3-2 Operations with Decimals 12.4 ÷ 6 = 36.5 ÷ 2 = 192.45 ÷ 50 = 2.0666 (repeating) 18.25 3.849

  20. Word problem… Section 3-2 Operations with Decimals Jill wants to buy a bottle of detergent. A 100-ounce bottle costs $6.49 and a 50-ounce bottle costs $3.99. Which would be the better buy ona cost per ounce basis? What are those amounts? The 50-ounce bottle costs of 0.0798 per ounce whilethe 100-ounce bottle has a cost of 0.0649 per ounce. The bigger bottle is a better buy. 6.49 ÷ 100 = 0.0649 3.99 ÷ 50 = 0.0798

  21. Change the divisor to a whole number by moving the decimal point to the right, counting the places as you go. • Use a caret () to show the new position of the decimal point. Divide by a decimal HOW TO: Section 3-2 Operations with Decimals • Move the decimal point in the dividend to the right as many places as you moved the divisor. • Place the decimal point for the quotient directly above the new decimal point for the dividend. • Divide as you would divide a whole number.

  22. More Division Examples… Section 3-2 Operations with Decimals 12.3 ÷ 0.06 = 15 ÷ 0.004 = 20.765 ÷ 0.08 = 205 3750 259.5625

  23. Word problem… Section 3-2 Operations with Decimals Seth Parker has an hourly rate of $12.27and his gross weekly pay was $441.72. How many hours did he work? 441.72 ÷ 12.27 = 36 hours Amber Sellnow has an hourly rate of $8.75 per hourand her gross weekly pay was $245.00 How many hours did she work last week? 28 hours 245.00 ÷ 8.75 =

  24. Learning Outcomes 3-3 • Convert a decimal toa fraction. • Convert a fraction toa decimal.

  25. Find the denominator: Write 1 followed by as many zeros as there are places to the right of the decimal point. Find the numerator: Use the digits without the decimal point. Reduce to lowest terms and/or write as a whole or mixed number. Convert a decimal to a fraction 3-3-1 Section 3-3 Decimal and Fraction Conversions

  26. Write 0.8 as a fraction. = Example… Section 3-3 Decimal and Fraction Conversions “8” becomes the numerator.There is one place to the right of the decimal point: Write 1 with a single zero: 10.“10” becomes the denominator. Reduce tolowest terms:

  27. Conversions Examples… Section 3-3 Operations with Decimals 0.75 converted to a fraction becomes… 0.625 converted to a fraction becomes… 0.25 converted to a fraction becomes…

  28. Write the numerator as the dividend and the denominator as the divisor. Divide the numerator by the denominator, taking the division out as many decimal places as necessary or desirable. In some cases, a repeating decimalwill be the quotient of the operation. You may indicate that it is a repeating decimal or round as needed. NOTE: Convert a fraction to a decimal 3-3-2 Section 3-3 Decimal and Fraction Conversions

  29. Write as a decimal. An Example… Section 3-3 Decimal and Fraction Conversions Divide 8 into 7.000. The result is 0.875 In this case the quotient is calleda terminatingdecimal. There is no remainder.

  30. More Conversions Convert to a decimal… Convert to a decimal… Convert to a decimal… Examples… Section 3-3 Operations with Decimals 205 3750 259.5625

  31. EXERCISES SET A

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  41. PRACTICE TEST

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