CHAPTER 3 – Decimals Instructor: Dr.Gehan Shanmuganathan.

CHAPTER 3 – Decimals

Instructor:

Dr.Gehan Shanmuganathan

Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel

© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved

Learning Outcomes

Read and write decimals.

Round decimals.

3-1



Our money system, based on the dollar, uses the decimal system.

Moving one place from right to left increases the value ten times.

Moving one place from left to right, causes the value of the number to become ten times smaller.

Read and write decimalsDecimal and Place-Value System

3-1-1Section 3-1



It is one part of a 10-part whole.

– 0.1 is read “one tenth.”

HOW TO: How much is .01?Decimal and Place-Value SystemSection 3-1

If this chart represented a dollar,the white segment would beequal to $0.10 (ten cents)



It separates the whole number part from the decimal part, as the number extends fromleft to right.

26.8 is read twenty-six and eight tenths.

– Or 26 point 8.

The decimal pointDecimal and Place-Value SystemSection 3-1

HOW TO:



The first place to the right of the decimal point is tenths—0.1

Second place is hundredths—0.01

Third place is thousandths—0.001

Fourth place is ten-thousandths.0.0001

Place value namesDecimal and Place-Value SystemSection 3-1

HOW TO:

…and so on



Read the whole number part first, saying “and” to indicate the beginning of the decimal part of the number.

Read or write a decimalDecimal and Place-Value SystemSection 3-1

HOW TO:

4.15— Four and fifteen hundredths

9.067—Nine and sixty-seven thousandths.

5.5—Five and five tenths.



When reading numbers that represent money amounts, read whole numbers as dollars.

– Decimal amounts are read as “cents.”

Reading decimals as money amountsDecimal and Place-Value SystemSection 3-1

HOW TO:

$46.57 is read “forty-six dollars and fifty-seven cents.”

Because 1 cent is one hundredthof a dollar, the words cent andhundredth have the same meaning.

TIP:



Read and write decimals

Find the digit in the specified place, and look at the next digit to the right.

– If this digit is less than 5, eliminate it, and all digitsto its right.

– If this digit is 5 or more, add 1 to the digit in the specified place, and eliminate all digits to its right.

Decimal and Place-Value SystemSection 3-1

HOW TO:



Round to the nearest tenth

Examples…

12.456

31,343.387

346.2778

12.5

31,343.4

346.3

Decimal and Place-Value SystemSection 3-1





Learning Outcomes

Add and subtract decimals.

Multiply decimals.

Divide decimals.

3-2



Add and subtract decimals

Add or subtract as though the numbers are whole numbers.

– Place the decimal point in the sum or differenceto align with the decimal point in the respective operation.

Operations with Decimals

3-2-1Section 3-2



Add and subtract decimalsOperations with Decimals

3-2-1Section 3-2

3. 4 7

- . 2 9

3. 1 8

.7 8 0

- .0 9 2

= .6 8 8

Attach extra zeros to the right end of each number so each number has the same quantity of digits.



Add & Subtract

Examples…

6.485 + 1.4 + 0.8 + 11.999 =

10.008 – 7.6 =

0.976 – 0.04217 =

20.684

Operations with DecimalsSection 3-2

2.408

0.93383



Multiply the decimal numbers as though theyare whole numbers.

Count the digits in the decimal parts of both decimal numbers.

Place the decimal point in the product so that there are as many digits in its decimal part as there are digits you counted in the previous step.

– If necessary, attach zeros to the left end of the product to place the decimal point accurately.

Multiply decimalsOperations with Decimals

3-2-2Section 3-2



Example…Operations with DecimalsSection 3-2

HOW TO:

3.45 x 4.082 =

How many places are there tothe right of the decimal point?

Five—so the product will have fiveplaces to the right of the decimal.

3.45 x 4.082 = 14.08290 The last zero can be droppedand the answer would be 14.0829.



Multiplication

Examples…

1.7 x 0.08 =

4.67 x 5.004 =

0.01 x 1.001=

0.136


23.36868

0.01001



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

– Divide as though the decimal points are whole numbers.

Divide decimalsOperations with Decimals

3-2-3Section 3-2



Division

Examples…

12.4 ÷ 6 =

36.5 ÷ 2 =

192.45 ÷ 50 =

2.0666 (repeating)


18.25

3.849



The 50-ounce bottle costs of 0.0798 per ounce whilethe 100-ounce bottle has a cost of 0.0649 per ounce.

The bigger bottle is a better buy.6.49 ÷ 100 = 0.0649 3.99 ÷ 50 = 0.0798

Word problem…Operations with DecimalsSection 3-2

Jill wants to buy a bottle of detergent. A 100-ounce bottle costs $6.49 and a 50-ounce bottle costs $3.99.

Which would be the better buy ona cost per ounce basis?

What are those amounts?



Change the divisor to a whole number by moving the decimal point to the right, counting the places as you go.

Divide by a decimalOperations with DecimalsSection 3-2

HOW TO:

Use a caret ( ) to show the new position of the decimal point.

Move the decimal point in the dividend to the right as many places as you moved the divisor.

Place the decimal point for the quotient directly above the new decimal point for the dividend.

Divide as you would divide a whole number.



More Division

Examples…

12.3 ÷ 0.06 =

15 ÷ 0.004 =

20.765 ÷ 0.08 =

205


3750

259.5625



36 hours

Word problem…Operations with DecimalsSection 3-2

Seth Parker has an hourly rate of $12.27and his gross weekly pay was $441.72.

How many hours did he work?

28 hours

Amber Sellnow has an hourly rate of $8.75 per hourand her gross weekly pay was $245.00

How many hours did she work last week?

441.72 ÷ 12.27 =

245.00 ÷ 8.75 =





Learning Outcomes

Convert a decimal toa fraction.

Convert a fraction toa decimal.

3-3



Find the denominator:

– Write 1 followed by as many zeros as there are places to the right of the decimal point.

Find the numerator:

– Use the digits without the decimal point.

Reduce to lowest terms and/or write as a whole or mixed number.

Convert a decimal to a fractionDecimal and Fraction Conversions

3-3-1Section 3-3



Write 0.8 as a fraction.

Example…Decimal and Fraction ConversionsSection 3-3

“8” becomes the numerator.

There is one place to the right of the decimal point:

Write 1 with a single zero: 10.

“10” becomes the denominator.

8

10 Reduce to

lowest terms:

4

5=



Conversions

Examples…

0.75 converted to a fraction becomes…




3

4

5

8

1

4



Write the numerator as the dividend and the denominator as the divisor.

Divide the numerator by the denominator, taking the division out as many decimal places as necessary or desirable.

Convert a fraction to a decimalDecimal and Fraction Conversions

3-3-2Section 3-3

In some cases, a repeating decimalwill be the quotient of the operation.

You may indicate that it is a repeating decimal or round as needed.

NOTE:



An Example…Decimal and Fraction ConversionsSection 3-3

Divide 8 into 7.000.

The result is 0.875

In this case the quotient is calleda terminating decimal.

There is no remainder.

Write as a decimal.7

8



More Conversions

Examples…Operations with DecimalsSection 3-3

Convert to a decimal…



1

2

3

8

2

3

205

3750

259.5625





EXERCISES SET A



EXERCISES SET A



EXERCISES SET A



EXERCISES SET A



EXERCISES SET A



EXERCISES SET A



EXERCISES SET A



EXERCISES SET A



EXERCISES SET A



EXERCISES SET A





PRACTICE TEST



PRACTICE TEST



PRACTICE TEST



PRACTICE TEST



PRACTICE TEST



PRACTICE TEST



Date post:	14-Jan-2016
Category:	Documents
Upload:	dwain-porter
View:	239 times
Download:	0 times

CHAPTER 3 – Decimals Instructor: Dr.Gehan Shanmuganathan.

Documents