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Chapter 3

Chapter 3. Decimals. #3. Learning Unit Objectives. Decimals. Rounding Decimals; Fraction and Decimal Conversions. LU3.1. Explain the place values of whole numbers and decimals; round decimals

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Chapter 3

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  1. Chapter 3 Decimals

  2. #3 Learning Unit Objectives Decimals Rounding Decimals; Fraction and Decimal Conversions LU3.1 Explain the place values of whole numbers and decimals; round decimals Convert decimal fractions to decimals, proper fractions to decimals, mixed numbers to decimals, and pure and mixed decimals to decimal fractions

  3. #3 Learning Unit Objectives Decimals Adding, Subtracting, Multiplying, and Dividing Decimals LU3.2 Add, subtract, multiply, and divide decimals Multiply and divide decimals by shortcut methods Complete decimal applications in foreign currency

  4. Table 3.1 - Bag of M&M’s Decimal Percent Color Fraction (hundredth) (hundredth) Yellow18 .33 32.73% 55 Red10 .18 18.18% 55 Blue 9 .16 16.36% 55 Orange 7 .13 12.73% 55 Brown 6 .11 10.91% 55 Green 5 .09 9.09% 55 Total55 1.00 100.00% 55 = 1

  5. Decimal place-value chart Figure 3.1 Whole Number Groups Decimal Place Values Ten Thousandths Hundredths Decimal Point Hundred Thousandths Thousandths Thousands Hundreds Tens Ones Tenths 1 10 1 . 100 1 . 1,000 1 . 10,000 1 . 100,000 1,000 100 10 1 and

  6. Rounding Decimals .3272727 .337272 Step 1. Identify the place value of the digit you want to round Step 3. Drop all digits to the right of the identified digit Step 2. Identify the digit to the right. If 5 or more, increase the identified digit by 1. If less than 5 do not change .33

  7. Rounding Decimals $.06 --------------------->The 6 is in the hundredths place value 1.527 --------------------> The 5 is in the tenths place value 2.8394 ------------------> The 4 is in the ten thousandths place value

  8. Converting Decimal Fractions to Decimals 2 Steps 1. Count the number of zeros in the denominator. 2. Place the numerator of the decimal fraction to the right of the decimal point the same number of places as you have zeros in the denominator. Do not go over the total number of denominator zeros. Fraction Decimal # of places 3 .3 1 10 3 .03 2 100 3 .003 3 1,000 3 .0003 4 10,000

  9. Converting Proper Fractions to Decimals 3 4 4 3.00 2.8 20 20 0 .75 EQUALS Step 1 .75

  10. Converting Mixed Numbers to Decimals 2 5 5 2.0 2.0 0 .4 (Step 1) 8 8 + .4 (Step 2) 8.4

  11. Converting Pure Decimals to Decimal Fractions Step 1 24 Step 2 24 1 .24 Places 2 Step 3 24 100

  12. Converting Mixed Decimals to Decimal Fractions 45 Step 1 45 1 Step 2 17.45 Places 2 4545 100 100 Step 3 =17

  13. Adding Decimals Add: 4 + 7.3 + 36.139 + .0007 + 8.22 4.0000 7.3000 36.1390 .0007 8.2200 55.6597

  14. Subtracting Decimals Subtract: 45.3 - 15.273 45.300 - 15.273 30.027

  15. Multiplying Decimals 8.52 (2 decimal places) x 6.7 (1 decimal places) 3 decimal places 57084 57.084 5 decimal places 3776 .03776 Need to add zero 2.36 x .016

  16. Dividing Decimals Step 1. Make the divisor a whole number by moving the decimal point to the right Step 2. Move the decimal point in the dividend to the right the same number of places as in step 1. If there are not enough places, add zeros to the right of the dividend. Step 3. Place the decimal point in the quotient above the new decimal point in the dividend. Divide as usual. Example 4.5 82.89 45. 828.9 18.42 45. 828.90 45 378 360 189 180 90 90

  17. Decimals Applications in Foreign Currency Key Currency Cross Rates $299 x .53230 = 159.1577 pounds Check 159.1577 pounds x 1.8785 = $298.98

  18. Shortcuts for Multiples of 10 Multiplication • Count the zeros in the multiplier • Move the decimal point the same • number of spaces to the right 6890 68.9 6.89 x 1000 6.89 x 10 6.89 x 100 689

  19. Shortcuts for Multiples of 10 Division • Count the zeros in the divisor • Move the decimal point the same • number of spaces to the left .00689 .689 6.89 / 1000 6.89 / 10 6.89 / 100 .0689

  20. Problem 3-62: Solution: $30,000 x 1.8785 = 56,355 pounds Check: 56, 355 x .53230 = $29,998 (due to rounding)

  21. Problem 3-69: Solution: 2 x $29.95 = $59.90 $0.145 x 410.85 = + $59.57 $119.47

  22. Problem 3-74: Solution: $14.99 + $3.10 + $3.75 = $ 21.84 110.8 sq. yards + 31.8 sq. yards + 161.9 sq. yards = x 304.5 $6,650.28

  23. Problem 3-76: Mustard A $.88 for 6 ounces $.88 ÷ 6 = $.15 Mustard B $1.61 for 12.5 ounces $1.61 ÷ 12.5 = $.13 Laundry Detergent A $2.00 for 37 ounces $2.00 ÷ 37 = $.05 Laundry Detergent B $2.37 for 38 ounces $2.37 ÷ 38 = $.06 Canned Tuna A $1.09 for 6 ounces $1.09 ÷ 6 = $.18 Canned Tuna B $1.29 for 8.75 ounces $1.29 ÷ 8.75 = $.15 Solution:

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