# Catherine Conway MATH 081.  Writing decimals in expanded form is similar to writing whole numbers in expanded form.  For example: Write 536.758 in.

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Catherine Conway MATH 081

 Writing decimals in expanded form is similar to writing whole numbers in expanded form.  For example: Write 536.758 in expanded form. 536 = 500 + 30 + 6

0.5 is “five tenths” 0.05 is “five hundredths” 0.005 is “five thousandths” Example: Write the following in words. 6.3 4.32 8.125 Six and three tenths Four and thirty-two hundredths Eight and one hundred twenty-five thousandths

For example: 0.006 2.15 64.2783

Round 2,349.785036 to the following place values. 1. Nearest hundred 2. Nearest tenths 3. Nearest thousands 4. Nearest thousandths 5. Nearest ten thousandths 2,300 2,349.8 2,000 2,349.785 2,349.7850

Catherine Conway MATH 081

 To add (or subtract) decimal numbers, we line up the decimal points and add (or subtract) as usual.  The decimal point in the result is written directly below the decimal point in the problem.

 Add: 23.42 + 5.413 + 925.7 23. 42 5. 413 925. 7 + 0 00 3 3 5 1 459 1. 1.Line up the decimal points 2.Put in zeros as place holders 3.Separate the columns (if needed) 4.Add (or subtract) as usual 5.Put the decimal in place.

 Subtract: 36.145 – 12.457 1.Line up the decimal points 2.Put in zeros as place holders 3.Separate the columns (if needed) 4.Add (or subtract) as usual 5.Put the decimal in place. 36. 145 12. 457 - 23 688.

 Add: 7 + 0.0012 + 4.2 + 0.03 7 0.0012 4.2 0.03 +.0000 000 00 11 2312 1.Line up the decimal points 2.Put in zeros as place holders 3.Separate the columns (if needed) 4.Add (or subtract) as usual 5.Put the decimal in place..

 Subtract: 4.7 – 2.0716 1.Line up the decimal points 2.Put in zeros as place holders 3.Separate the columns (if needed) 4.Add (or subtract) as usual 5.Put the decimal in place. 4.7 2.0716 - 2 6284 000.

 Add: 4.59 + (-9.33) 9.33 4.59 - 4.74 - 1.Use Rule #2 – Subtract smaller number from larger 2.Line up the decimal points 3.Put in zeros as place holders 4.Separate the columns (if needed) 5.Add (or subtract) as usual 6.Put the decimal in place. 7.Use the sign of the number with the larger absolute value

Catherine Conway Math 081

 Multiply as you would if the decimal points were not there.  Place the decimal point in the answer so that the number of digits to its right is equal to the total number of digits to the right of the decimal points in the original two numbers in the problem.

 page 258 #8, 16, 18, 24, 28 8. (-8.9)(-0.2) 16. 7(0.005) 18. 963.8 x 0.24 24. 12,345 x 1,000 28. 1.23 x 100,000 -8.9 x -0.2 1 78. 0.005 x 7 35. 0 0 38552. +19276 0 231312,000 12,345 00000 123.,

 We can use rule for order of operations to simplify expressions involving decimal numbers and addition, subtraction, and multiplication. Parentheses, Exponents, Multiplication, Divisions, Addition, Subtraction

 Page 258 #34, 36, 42, 44 34. -4.04(0.07 + 0.09) 36. (9.2 + 0.01)(3.5 + 0.03) 42. 7.89 – 2(0.31 + 0.76) 44. 3.6 + 15(-2.1) 2 Parentheses (add), multiply Parentheses (add) 2 sets, multiply Parentheses (add), multiply, subtract Exponents, multiply, add -4.04(0.16) -0.6464 (9.21)(3.53) 32.5113 7.89 – 2(1.07) 7.89 – 2.14 5.75 3.6 + 15(4.41) 3.6 + 66.15 69.75

 58. Car Rental: Suppose it costs \$15 per day and \$0.21 per mile to rent a car. What is the total bill if the car is rented for 2 days and is driven 120 miles?  60. A student earns \$8.56 for each of the first 40 hours she works in one week and \$12.84 in overtime pay for each additional hour she works in the same week. How much money will she make if she works 44 hours in one week? 15(2) = total cost for 2 days 0.21(120) = total cost for miles 15(2) + 0.21(120) 30 + 25.20 \$55.20 total bill 8.56(40) = earning for the week 12.84(4) = additional earning 8.56(40) + 12.84(4) 342.4 + 51.36 \$393.76 total bill

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