5.1 – Introduction to DecimalsDecimal Notation and Writing Decimals.

2, 4 5 7, 8 3 2 . 8 3 0 9 4

ones

tens

hund

reds

thou

sand

s

ten-

thou

sand

s

hund

red-

thou

sand

s

mill

ions

tent

hs

hund

redt

hs

thou

sand

ths

ten-

thou

sand

ths

hund

red-

thou

sand

ths

4. – Solving Equations with Fractions

Write each number in words.

5.1 – Introduction to DecimalsDecimal Notation and Writing Decimals.

0.06 Six hundredths

Negative two hundred and seventy-three thousandths

Eight hundred twenty-nine ten-thousandths

Eighty-seven and thirty-one hundredths

-200.073

0.0829

87.31

52.1085

1493.62

Fifty-two and one thousand eighty-five ten-thousandths

One thousand four hundred ninety-three and sixty-two hundredths

4. – Solving Equations with Fractions

Write each decimal in standard form.

5.1 – Introduction to DecimalsDecimal Notation and Writing Decimals.

500.96Five hundred and ninety-six hundredths

Thirty-nine and forty-two thousandths

Negative eight hundred seven and twenty-five ten-thousandths

Twelve thousand thirty-seven and two hundred ninety-eight thousandths

39.042

-807.0025

12,037.298

51

64

241

32

1000

29

Write the following decimals as fractions/mixed numbers in simplest form.

100

97

64

1001000

5.1 – Introduction to DecimalsDecimal Notation and Writing Decimals.

29.97

0.241

0.032

0.51

64.8 -209.986

4

125

810

45

2091000

986

209500

493

Compare digits in the same place, when determining which number is larger.

5.1 – Introduction to DecimalsComparing Decimals

When two digits are not the same value, the larger digit is the larger decimal.

26.208 26.28 0.12 0.026

0.0065 0.00065 3.4251 3.4249

-0.562 -0.652 -0.039 -0.0309

<

>

>

>

> <

Use < or > to make a true statement

Locate the digit to the right of the requested place value.

5.1 – Introduction to DecimalsRounding Decimals

If the digit to the right is 5 or greater, round the place value up one and drop remaining digits.

482.7817 Round to the nearest thousandth 482.782

0.7522 0.8

752.883 750

If the digit to the right is less than 5, the place value remains and the remaining digits are dropped.

Round to the nearest tenth

Round to the nearest tens

3.141592 3.14Round to the nearest hundredth

5.2 – Adding and Subtracting Decimals

Zeros placed at the end of the last digit in a decimal do not change the value of the decimal.

Are the values the same?

0.030.00030.003000.3

NO

0.00300000.0030000.00300.00300

YES

0.0030.0030.0030.003

YES

5.2 – Adding and Subtracting Decimals1) Write the numbers so the decimal points line up vertically.

2) Place zeros after the last digit to assist in adding or subtracting the decimals.

3) Add or subtract the decimal places like whole numbers.Examples:

19.525.371

0+

19.52 + 5.371

24.891

40.0817.612

0+

40.08 + 17.612

57.692

5.2 – Adding and Subtracting DecimalsExamples:

0.125422.800+

0.125 + 422.8

422.925

1926.47

.00+

19 + 26.47

45.47

34.567129.43

0

+

34.567 + 129.43 + 2.8903

2.890300

3788.661

11.2146.013

0

+

11.21 + 46.013 + 362.526

362.526974.914

5.2 – Adding and Subtracting DecimalsExamples:

6.73.92

0-

6.7 – 3.92

8

7329.31

.00-

73 – 29.31

9

-5.4-9.6

-

-5.4 – 9.6

015.

-9.927.12

7.12 + (-9.92)

08.2-

7.2 6.34

5.2 – Adding and Subtracting DecimalsExamples:

25.9119.204

0-

19.204 from 25.91

6

0-

7

11.610.87

Evaluate y – z if y = 11.6 and z = 10.87

30.

7.6 0

5.2 – Adding and Subtracting DecimalsExamples:

y – 4.3 = 7.84

Is 12.14 a solution of the equation y – 4.3 = 7.84?

4.3

7.84

0-12.14

4

12.14 is a solution.

=8.7

12.14 – 4.3 = 7.84

5.2 – Adding and Subtracting DecimalsExamples:

-4.30y-20.18y

y-

-4.3y + 7.8 – 20.18y + 14.602

8

7.814.602

00

-24.48y + 22.402

22 04.24.42

5.2 – Adding and Subtracting DecimalsEstimation – a process to check if an answer is reasonable.

58.1326.97

0+

58.1 + 326.97

7

60 + 330

33060

0.5 390

Actual (Exact) Estimate

83

16.080.921

0-

16.08 – 0.921

9

16 – 1

116

51. 15

Actual (Exact) Estimate

51

-

5.3 – Multiplying Decimals1) Multiply the decimals as thought they are whole numbers.

2) Add the number of decimal places in each term.

3) From the last digit of the product, count to the left and place the decimal after that numbered term.Examples:

6960.62

21576

x34.8

2088

3 decimal places

21.576

448727

17307

x0.0641

1282

4 decimal places

1.7307

5.3 – Multiplying DecimalsExamples:

657-0.9

6.57

x7.3

2 decimal places27

7.3

657

x-0.9

63

2 decimal places

6.57

5.3 – Multiplying DecimalsActual (Exact)

272342.89

874514

x30.26

4 decimal places

87.4514

903x

30

242086052

Estimate

5.3 – Multiplying DecimalsExamples:

-6 (-5.5)

Is -5.5 a solution of the equation: – 6x = 33?

6

33

330x

5.5

1 decimal place=

-5.5 is a solution.

33.0

5.3 – Multiplying DecimalsA garden contains 60.5 square yards of space for planting. The fertilizer to be used on the garden suggests a spreading rate of 5.6 ounces per square yard. How many ounces of fertilizer are needed?

ounces

36305.6

338.8

x60.5

2 decimal places338.80

302533880

5.3 – Circumference of a Circle

Blue line = DiameterRed line = Radiusd = 2r

Circumference – the length around the edge of a circle.

C = d

r

d

C = 2 r

or

5.3 – Circumference of a Circle

Find the circumference of a circle whose diameter is 7 meters.( Use 3.14 as an approximation of .)

21987

meters

x3.14

2 decimal places

21.98

C = d C = 2 ror

C = 3.14 (7)

5.3 – Circumference of a Circle

Find the circumference of a circle whose radius is 2.5 feet.( Use 3.14 as an approximation of .)

6282x

3.14

2 decimal places

6.28

C = d C = 2 ror

C =2 (3.14) (2.5)

31402.5

15.7

x6.28

3 decimal places

15.700

125615700

feet