5.1 – Introduction to Decimals

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5.1 – Introduction to Decimals. Decimal Notation and Writing Decimals. 2 , 4 5 7 , 8 3 2 . 8 3 0 9 4. tens. o nes. tenths. millions. hundreds. thousands. hundredths. thousandths. ten-thousands. ten-thousandths. hundred-thousands. hundred-thousandths.

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5.1 – Introduction to Decimals

Decimal Notation and Writing Decimals.

2, 457, 83 2 . 83094

tens

ones

tenths

millions

hundreds

thousands

hundredths

thousandths

ten-thousands

ten-thousandths

hundred-thousands

hundred-thousandths

5.1 – Introduction to Decimals

4. – Solving Equations with Fractions

Decimal Notation and Writing Decimals.

Write each number in words.

0.06

Six hundredths

-200.073

Negative two hundred and seventy-three thousandths

0.0829

Eight hundred twenty-nine ten-thousandths

87.31

Eighty-seven and thirty-one hundredths

52.1085

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

1493.62

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

5.1 – Introduction to Decimals

4. – Solving Equations with Fractions

Decimal Notation and Writing Decimals.

Write each decimal in standard form.

Five hundred and ninety-six hundredths

500.96

Thirty-nine and forty-two thousandths

39.042

Negative eight hundred seven and twenty-five ten-thousandths

-807.0025

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

12,037.298

5.1 – Introduction to Decimals

Decimal Notation and Writing Decimals.

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

0.51

0.241

0.032

29.97

64.8

-209.986

5.1 – Introduction to Decimals

Comparing Decimals

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

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

Use<or>to make a true statement

26.208

<

26.28

0.12

>

0.026

0.00065

3.4251

0.0065

>

>

3.4249

-0.652

-0.039

<

-0.562

>

-0.0309

5.1 – Introduction to Decimals

Rounding Decimals

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

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

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

482.7817

Round to the nearest thousandth

482.782

0.7522

Round to the nearest tenth

0.8

3.141592

Round to the nearest hundredth

3.14

752.883

Round to the nearest tens

750

5.2 – Adding and Subtracting Decimals

Are the values the same?

0.0030000

0.03

0.003

0.003000

0.0003

0.003

0.0030

0.00300

0.003

0.00300

0.3

0.003

YES

YES

NO

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

5.2 – Adding and Subtracting Decimals

1) 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:

19.52 + 5.371

40.08 + 17.612

19.52

0

40.08

0

+

+

5.371

17.612

24.891

57.692

5.2 – Adding and Subtracting Decimals

Examples:

0.125 + 422.8

19 + 26.47

0.125

19

.00

+

00

422.8

+

26.47

422.925

45.47

11.21 + 46.013 + 362.526

34.567 + 129.43 + 2.8903

11.21

0

34.567

0

129.43

00

46.013

+

+

2.8903

362.526

9

.

1

6

8

3

.

9

1

6

4

4

8

7

7

5.2 – Adding and Subtracting Decimals

Examples:

6.7 – 3.92

73 – 29.31

0

6.7

73

.00

-

-

3.92

29.31

4

3

6

2

9

.

8

.

7

7.12 + (-9.92)

-5.4 – 9.6

-9.92

-5.4

7.12

-9.6

.

-

8

2

0

-

15

.

0

5.2 – Adding and Subtracting Decimals

Examples:

19.204 from 25.91

0

25.91

-

19.204

6

6

.

7

0

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

0

11.6

-

10.87

0

7

3

.

5.2 – Adding and Subtracting Decimals

Examples:

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

y – 4.3 = 7.84

12.14 – 4.3 = 7.84

12.14

-

4.3

0

.

8

4

=

7

7.84

12.14 is a solution.

5.2 – Adding and Subtracting Decimals

Examples:

-4.3y + 7.8 – 20.18y + 14.602

-4.30y

00

7.8

-20.18y

14.602

-

8

0

2

4

2

.

4

y

2

2

.

4

-24.48y + 22.402

5.2 – Adding and Subtracting Decimals

Estimation – a process to check if an answer is reasonable.

Actual (Exact)

Estimate

58.1 + 326.97

60 + 330

58.1

60

0

330

+

326.97

390

7

.

0

5

8

3

Actual (Exact)

Estimate

16.08 – 0.921

16 – 1

16

16.08

0

1

-

0.921

-

15

1

9

5

.

5

1

5.3 – Multiplying Decimals

1) 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:

0.0641

34.8

x

0.62

x

27

696

4487

1282

2088

17307

21576

4 decimal places

3 decimal places

1.7307

21.576

5.3 – Multiplying Decimals

Examples:

-0.9

7.3

x

7.3

x

-0.9

27

657

63

2 decimal places

657

6.57

2 decimal places

6.57

5.3 – Multiplying Decimals

Estimate

Actual (Exact)

30

30.26

x

3

x

2.89

90

27234

24208

6052

874514

4 decimal places

87.4514

5.3 – Multiplying Decimals

Examples:

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

-6 (-5.5)

5.5

x

6

330

1 decimal place

=

33.0

33

-5.5 is a solution.

5.3 – Multiplying Decimals

A 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?

60.5

5.6

x

3630

3025

33880

2 decimal places

338.80

ounces

338.8

5.3 – Circumference of a Circle

Blue line = Diameter

r

d

d= 2r

Circumference – the length around the edge of a circle.

C =  d

or

C = 2  r

5.3 – Circumference of a Circle

C =  d

or

C = 2  r

Find the circumference of a circle whose diameter is 7 meters.

( Use 3.14 as an approximation of .)

C = 3.14 (7)

3.14

x

7

2198

2 decimal places

21.98

meters

5.3 – Circumference of a Circle

C =  d

or

C = 2  r

Find the circumference of a circle whose radius is 2.5 feet.

( Use 3.14 as an approximation of .)

C =2 (3.14) (2.5)

3.14

6.28

x

2

2.5

x

628

3140

2 decimal places

1256

15700

6.28

3 decimal places

15.700

15.7

feet