Chapter 2 decimal.ppt

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Business Math
Chapter 2: Decimals

Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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3.1 Decimals and
the Place Value System
 Read and write decimals
 Round decimals
1.2345 rounded to the nearest tenth is 1.2

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3.1.1 Read and write decimals
 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 digit to become ten times smaller.

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How much is 0.1?
 It is one part of a 10-part
whole.
 0.1 is read “one tenth”
If this chart represented a
dollar, the white segment
would be equal to $0.10.

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The decimal point
 Separates the whole number part from the
decimal part, as the number extends from left to
right.
 34.7 is read thirty four and seven tenths
or 34 point 7.

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Place value names
 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)
and so on.

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How to read or write a decimal
 3.12 Three and twelve hundredths
 9.067 Nine and sixty-seven thousandths.
 4.5 Four and five tenths.
Read the whole number part first, saying “and”
to indicate the beginning of the decimal part of
the number.

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Reading decimals as
money amounts
 When reading numbers that represent money
amounts, read whole numbers as dollars.
 Decimal amounts are read as “cents.”
 $35.98 is read “thirty–five dollars and 98 cents.”

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3.1.2 Round to a specific
decimal place
1. Find the digit in the specified place.
2. Look at the next digit to the right.
 If this digit is less than 5, eliminate it and all
digits to its right.
 If the digit is 5 or more, add 1 to the digit in
the specified place, and eliminate all digits to
its right.

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Try these examples
Round to the nearest tenth
 12.456
 12.5
 31,343.387
 31,343.4
 346.2778
 346.3

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3.2 Operations with decimals
 Add and subtract decimals
 Multiply decimals
 Divide decimals
3.234 + 6.8 = ?

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Add and subtract decimals
 Write the numbers in a vertical column, aligning
digits according to their places.
 Attach extra zeros to the right end of each
number so each number has the same quantity
of digits.
 Add or subtract as though the numbers are
whole numbers.
 Place the decimal point in the sum or difference
to align with the decimal point in the respective
operation.

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Be orderly to avoid mistakes.
3. 4 7
- . 2 9
3. 1 8

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Add zeros where necessary
.7 8 0
- .0 9 2
= .6 8 8

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Try these examples.
(Without using your calculator)
 7.098 + 2.6 + 0.8 + 13.999 =
 24.497
 10.008 – 7.6 =
 2.408
 .976 - .04217 =
 .93383

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3.2.2 Multiply decimals
 Multiply the decimal numbers as though they are
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.

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Look at this example.
3.45 x 4.082 =
 How many places are there to the right of the
decimal point?
 Five; so, the answer will have five places to the
right of the decimal.
 The answer is 14.08290
 The last zero can be dropped and the answer
would be 14.0829.

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Try these examples
 2.4 x .06 =
 0.144
 3.07 x 8.008 =
 24.58456
 .01 x 1.001=
 0.01001

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3.2.3 Divide decimals
Divide a decimal by a whole number:
 Place a decimal point for the quotient directly
above the decimal point in the dividend.
 Divide as though the decimal points are whole
numbers.
3.4 divided by 3 = ?

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Try these examples
 12.4 ÷ 6 =
 2.06 (repeating)
 36.5 ÷ 2 =
 18.25
 192.45 ÷ 50 =
 3.849

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Try this word problem
 Jill wants to buy a bottle of detergent. If a 100-
ounce bottle costs $6.49 and a 50- ounce bottle
costs $3.99, which would be the better buy on
cost per ounce basis? What are those
amounts?
Answer: The 50 - ounce bottle has a cost of
.0798 per ounce while the 100-ounce bottle has
a cost of .0649 per ounce. The bigger bottle is a
better buy.

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

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Try these examples.
Without using your calculator)
 12.3 ÷ .06 =
 205
 15 ÷ .004 =
 3,750
 20.765 ÷ .08 =
 259.5625

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Try these word problems.
 Bill Sullivan has an hourly rate of $14.32 and his
gross weekly pay was $572.80. How many
hours did he work?
 40 hours
 Jan Stevens has an hourly rate of $7.75 per
hour and her gross weekly pay was $193.75.
How many hours did she work last week?
 25 hours

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 Convert a decimal to a fraction.
 Convert a fraction to a decimal.
1/2 = 50%
25% = 1/4
3.3 Decimal and Fraction
Conversions

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Convert a decimal to a fraction
 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.

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Here’s an example.
 Write 0.8 as a fraction
 “8” becomes the numerator.
 There is one place to the right of the decimal
point: 1 + 0 = 10.
 “10” becomes the denominator.
 0.8 = 8/10
 Reduce to lowest terms.
 4/5

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Try these examples.
 0.75 converted to a fraction becomes…
 ¾
 ⅝
 ¼

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Convert a fraction to a decimal
 Write the numerator as a 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.
 Note: In some cases, a repeating decimal will
be the quotient of the operation. You may
indicate that it is a repeating decimal or round as
needed.

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Here’s an example.
 Write ⅞ as a decimal.
 Divide 8 into 7.000.
 The result is 0.875
 In this case the quotient is called a terminating
decimal; there is no remainder.

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Try these examples.
 Convert ½ to a decimal.
 0.5
 Convert ⅜ to a decimal.
 0.375
 Convert ⅔ to a decimal.
 0.6666(repeating) or 0.67

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