OBJECTIVES

R.3 Decimal Notation

Slide 2Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

a Convert from decimal notation to fraction notation.b Add, subtract, multiply, and divide using decimal

notation.c Round numbers to a specified decimal place.

The decimal notation 42.3245 means

4 tens + 2 ones + 3 tenths + 2 hundredths + 4 thousandths + 5 ten-thousandths

R.3 Decimal Notation

a Convert from decimal notation to fraction notation.

Slide 3Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

The decimal notation 42.3245 means

We read this number as

“Forty-two and three thousand two hundred forty-five ten-thousandths.”

The decimal point is read as “and”.

R.3 Decimal Notation

a Convert from decimal notation to fraction notation.

Slide 4Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

4.98

4.98

2 zeros

2 places

Move 2 places.

498

100

a) Count the number of decimalplaces.

b) Move the decimal point thatmany places to the right.

c) Write the result over a denominator with that numberof zeros.

R.3 Decimal Notation

To Convert from Decimal to Fraction Notation

Slide 5Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE

9240.

0924

100

3 places3 zeros

0.924.

Solution

R.3 Decimal Notation

a Convert from decimal notation to fraction notation.

A Write fraction notation for 0.924. Do not simplify.

Slide 6Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

What do we do?

EXAMPLE

SolutionTo write as a fraction:

177717

0.77

10

2 zeros

2 places

17.77.

R.3 Decimal Notation

a Convert from decimal notation to fraction notation.

B Write 17.77 as a fraction and as a mixed numeral.

Slide 7Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE

Solution

7717.77 17

100

To write as a mixed numeral, we rewrite the whole number part and express the rest in fraction form:

R.3 Decimal Notation

a Convert from decimal notation to fraction notation.

B Write 17.77 as a fraction and as a mixed numeral.

Slide 8Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

8.679.Move

3 places.

3 zeros

8679

1000a) Count the number of zeros.

b) Move the decimal point thatnumber of places to the left. Leaveoff the denominator.

R.3 Decimal Notation

Converting to Decimal Notation when the Denominator is a Power of Ten

Slide 9Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE53

.10

53

105.3. 53

105.3

1 place1 zero

Solution

R.3 Decimal Notation

a Convert from decimal notation to fraction notation.

C Write decimal notation for

Slide 10Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

Adding with decimal notation is similar to adding whole numbers.

First we line up the decimal points so that we can add corresponding place-value digits.

R.3 Decimal Notation

b Add, subtract, multiply, and divide using decimal notation.

Slide 11Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

Add the digits from the right.

If necessary, we can write extra zeros to the far right of the decimal point so that the number of places is the same.

R.3 Decimal Notation

b Add, subtract, multiply, and divide using decimal notation.

Slide 12Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLESolutionLine up the decimal points and write extra zeros.

R.3 Decimal Notation

b Add, subtract, multiply, and divide using decimal notation.

D Add: 4.31 + 0.146 + 14.2

Slide 13Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

4.310.146

14.21

0

008.656

EXAMPLESolution Line up decimal points and subtract, borrowing if

necessary.

3 4 . 0 7 0 0 – 4 . 0 0 5 2

84600 .3

6 91

R.3 Decimal Notation

b Add, subtract, multiply, and divide using decimal notation.

E Subtract: 34.07 – 4.0052

Slide 14Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE

5717 0 .5

9 9 103

Solution

5 7 4 . 0 0 0 – 3 . 8 2 5

R.3 Decimal Notation

b Add, subtract, multiply, and divide using decimal notation.

F Subtract 574 – 3.825

Slide 15Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

a) Ignore the decimal points, and multiply as whole numbers.

b) Place the decimal point in the result of step (a) by adding the number of decimal places in the original factors.

R.3 Decimal Notation

Multiplication with Decimal Notation

Slide 16Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLESolution: Ignore the decimal points and multiply as if both factors are integers then place the decimal point.

8 5 . 1 × 7 . 3 2 5 5 3 5 9 5 7 0 6 2 1 2 3

13

1 decimal place1 decimal place

2 decimal places.

R.3 Decimal Notation

b Add, subtract, multiply, and divide using decimal notation.

G Multiply 7.3 85.1.∙

Slide 17Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

a) Place the decimal point in the quotient directly above the decimal point in the dividend.

b) Divide as whole numbers.

R.3 Decimal Notation

Dividing When the Divisor Is a Whole Number

Slide 18Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE

26 91.2678 132 130 26 26 0

3.51

place the decimal pointSolution

R.3 Decimal Notation

b Add, subtract, multiply, and divide using decimal notation.

H Divide 91.26 ÷ 26.

Slide 19Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

a) Move the decimal point in the divisor as many places to the right as it takes to make it a whole number. Move the decimal point in the dividend the same number of places to the right and place the decimal point in the quotient.

b) Divide as whole numbers, inserting zeros if necessary.

R.3 Decimal Notation

Dividing When the Divisor Is not a Whole Number

Slide 20Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLESolution

7.872 ÷ (9.6) = 0.82.

9.6 7.872 Multiply the divisor by 10 (move the decimal point 1 place). Multiply the same way in the dividend (move the decimal point 1 place).

.8296. 78 72

768

192

192

0

.

R.3 Decimal Notation

b Add, subtract, multiply, and divide using decimal notation.

I Divide: 7.872 ÷ 9.6.

Slide 21Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE7

.25

7

25

7 4

25 4

28

100 0.28

Solution

R.3 Decimal Notation

b Add, subtract, multiply, and divide using decimal notation.

J Find decimal notation for

Slide 22Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE 1.

12Solution Divide 1 ÷ 12

R.3 Decimal Notation

b Add, subtract, multiply, and divide using decimal notation.

K Find decimal notation for

(continued)

Slide 23Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

0.083312 1.0000

0100 96 0 36 0 36 4

4

4

EXAMPLE 1.

12Since 4 keeps reappearing as a remainder, the digits repeat and will continue to do so; therefore,

10.08333...

12

10.083.

12

The dots indicate an endless sequence of digits in the quotient. The dots are often replaced by a bar to indicate the repeating part.

R.3 Decimal Notation

b Add, subtract, multiply, and divide using decimal notation.

K Find decimal notation for

Slide 24Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE0.4545

11 5.000044 0 55 0 44 0 55

6

5

6

5

5.

11

50.454545..., or 0.45

11

Solution5 ÷ 11

Since 6 and 5 keep reappearing as remainders, the sequence of digits “45” repeats in the quotient, and

R.3 Decimal Notation

b Add, subtract, multiply, and divide using decimal notation.

L Find decimal notation for

Slide 25Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

To round to a certain place:a) Locate the digit in that place. b) Consider the digit to its right.c) If the digit to the right is 5 or higher, round up, if the

digit to the right is less than 5, round down.

R.3 Decimal Notation

Rounding Decimal Notation

Slide 26Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLESolutiona. Locate the digit in the tenths place.

0.072b. Consider the next digit to the right.

c. Since that digit, 7 is greater than 5, round up to 0.1

R.3 Decimal Notation

c Round numbers to a specified decimal place.

M Round 0.072 to the nearest tenth.

Slide 27Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLESolutiona. Locate the digit in the hundredths place.

34.7824b. Consider the next digit to the right.

c. Since that digit, 2 is less than 5, we round down to 34.78

R.3 Decimal Notation

c Round numbers to a specified decimal place.

N Round 34.7824 to the nearest hundredth.

Slide 28Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE

R.3 Decimal Notation

c Round numbers to a specified decimal place.

O Round 478.3469 to the nearest thousandth, hundredth, tenth, one, ten, hundred, and thousand.

(continued)

Slide 29Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE

4 7 8 . 3 4 6 9

thousandth 4 7 8 . 3 4 7

hundredth 4 7 8 . 3 5

tenth 4 7 8 . 3

one 4 7 8 .

ten 4 8 0 .

hundred 5 0 0 .

thousand 0 .

Solution

R.3 Decimal Notation

c Round numbers to a specified decimal place.

O Round 478.3469

Slide 30Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.