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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
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
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
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
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)
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
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:
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
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
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
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.
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
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:
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
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:
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
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
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
Learning Outcomes
Add and subtract decimals.
Multiply decimals.
Divide decimals.
3-2
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
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
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
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.
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
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
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
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
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
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.
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
Multiplication
Examples…
1.7 x 0.08 =
4.67 x 5.004 =
0.01 x 1.001=
0.136
Operations with DecimalsSection 3-2
23.36868
0.01001
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
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
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
Division
Examples…
12.4 ÷ 6 =
36.5 ÷ 2 =
192.45 ÷ 50 =
2.0666 (repeating)
Operations with DecimalsSection 3-2
18.25
3.849
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
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?
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
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.
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
More Division
Examples…
12.3 ÷ 0.06 =
15 ÷ 0.004 =
20.765 ÷ 0.08 =
205
Operations with DecimalsSection 3-2
3750
259.5625
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
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 =
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
Learning Outcomes
Convert a decimal toa fraction.
Convert a fraction toa decimal.
3-3
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
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
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
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=
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
Conversions
Examples…
0.75 converted to a fraction becomes…
0.625 converted to a fraction becomes…
0.25 converted to a fraction becomes…
Operations with DecimalsSection 3-3
3
4
5
8
1
4
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
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:
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
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
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
More Conversions
Examples…Operations with DecimalsSection 3-3
Convert to a decimal…
Convert to a decimal…
Convert to a decimal…
1
2
3
8
2
3
205
3750
259.5625
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
EXERCISES SET A
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
EXERCISES SET A
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
EXERCISES SET A
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
EXERCISES SET A
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
EXERCISES SET A
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
EXERCISES SET A
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
EXERCISES SET A
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
EXERCISES SET A
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
EXERCISES SET A
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
EXERCISES SET A
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
PRACTICE TEST
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
PRACTICE TEST
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
PRACTICE TEST
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
PRACTICE TEST
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
PRACTICE TEST
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved
PRACTICE TEST
Business Math, Ninth EditionCheryl Cleaves, Margie Hobbs & Jeffrey Nobel
© 2012 Pearson Education, Inc.Upper Saddle River, NJ 07458 All Rights Reserved