FLC

Ch 5

Math 20 Arithmetic Sec 5.1: Introduction to Decimals Consider the decimal number 13.4238 and identify its three components: whole number part, decimal point, and fractional part. Finish the expanded form:

Combine the fractions:

Write the number in words:

We use fractions to represent parts of a whole. The decimal system is another way to represent the same thing.

Decimal Place Value Chart

_____ _____ _____ _____ _____ _____ _____ . _____ _____ _____ _____ _____ _____ _____ 

Ex 1 Identify the place value of each underlined digit. a) 971.54 b) 0.004

c) 5.60

Ex 2 Tell how to read each decimal in words. a) 0.6 b) 0.46

c) 0.05

d) 0.0003

Use “and” only where there’s a decimal.

e) 100.0703

f) 5.409

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FLC

Ch 5

Ex 3 Write each decimal number in expanded form. Next, combine the whole number part and the sum of the fractional parts. a)

Ex 4

b)

Pronounce and write the decimal number in words.

a)

Ex 5

c)

b)

c) PP

Convert the given decimal to a mixed fraction. Do not simplify your answer.

a)

b)

c)

d)

0.07

12.21

0.101

0.007

e)

f)

g)

h)

1.3717

0.5

12.6000

0.85

i)

j)

k)

l) PP

3.05

0.225

420.0802

0.006

Ex 6

Convert the given decimal to an improper fraction. Do not simplify your answer.

a)

b)

c)

d)

3.1

5.27

2.893

1.271

Ex 7

Convert the given decimal to a fraction. Reduce your answer to lowest terms.

a)

b)

c)

d)

0.38

0.88

0.123

1.271

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FLC

Ch 5

Warning!  

Never move decimal when rounding. When rounding decimals, the last digit must match with the place you are rounding to. For instance, 0.299 rounded to the nearest tenth is 0.3 but rounded to the nearest hundredth is 0.30.

Ex 8 Round to the nearest thousandth. a) 0.33432 b) 8.00851

Ex 9

c) 8.00041

e) 10.8995

Round 399 to the nearest hundred and 0.399 to the nearest tenths.

Ex 10 Round to the place indicated. a) 5.8903; hundredth

b) 11.0299; tenth

Ex 11 Round to the nearest cent. a) $14.595

b) $578.0663

Ex 12 Round to the nearest dollar. a) $29.10 b) $990.91

c) 0.96; tenth

c) $0.0548

c) $0.55

Ex 13 Write each number. a) Two hundred ten thousandths

Ex 14

d) 10.9995

d) $1.08

e) $0.35

b) Two hundred ten-thousandths

Determine which of the two statements are true.

a)

b)

or

c)

or

or

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FLC

Ch 5 Sec 5.2: Adding and Subtracting Decimals When adding or subtracting decimals, be sure

to LINE UP the decimals.

(We do NOT need to do this when multiplying or dividing.)

Ex 15 a)

Find each sum. Check that your answer is reasonable. b)

c)

PP

Ex 16 Subtract. a) from

Check answers using addition.

b)

c)

less

d)

PP

Ex 17 a) PP

Add or subtract to find the exact answer. b) Find the difference between meters

Ex 18

Evaluate. (Add or subtract.)

a)

b)

c)

(

)

meters and

d)

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FLC e)

Ch 5 (

f)

)

g)

i)

h)

j)

|

Ex 19

(

)|

(

k)

(

(

))

|

Sec 5.3: Multiplying Decimals Multiply using fractions first (do not simplify), then using decimals.

(

)

Do we need to line up the decimals when multiplying or dividing decimals? _____________ Review:

Do we need to convert mixed fractions to improper fractions when adding/subtracting?______ Do we need to convert mixed fractions to improper fractions when multiplying/dividing?_____ Ex 20 a)

Multiply.

c) (

b)

)(

)

Is answer reasonable?

d) (

)

)

e) (

)(

)(

)

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|

FLC f) (

Ch 5 )(

)

h) (

)(

k) (

)(

Ex 21 a) (

g)

)

)

(

)

i)

(

)

j)

l) (

Estimate the answer. Then find the exact answer. )( ) b) PP (

)(

)

)(

)

Ex 22 Without multiplying, determine which problem is easier to complete. Explain. ( )( ) vs ( )( )

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FLC Ex 23

Ch 5 Given

and

, evaluate the expression

.

The Circle A circle is the collection of all points equidistant from a given point 𝑂, called the center of the circle.

The segment joining any point on the circle to the center is called a radius of the circle. If two points on a circle are connected with a line segment, that segment is called a chord of the circle. If the chord passes through the center of the circle, the chord is called the diameter of the circle. Note that 𝒅 𝟐𝒓.

The length of the circle is called its circumference, which we usually denote as 𝐶. Whenever the circumference of a circle is divided by its diameter, the result is the constant 𝜋. Formulas: 𝐶 𝜋 𝐶 𝜋𝑑 𝑪 𝟐𝝅𝒓 𝑑 Ex 24 A circle has diameter of 15.49 inches. Find the exact area of the circle. Next, use the area, correct to the nearest hundredth of a square inch.

to estimate

Ex 25 How much would it cost to paint a circular tabletop of diameter 15.49 inches if it costs $2/in 2? Provide the exact answer and estimate.

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FLC

Ch 5

Sec 5.4: Dividing Decimals Recall Different notation for division and divisor, dividend, and quotient

Ex 26

Divide.

Check answers by multiplying.

a)

b)

c)

4 93.6

Ex 27

(

)

Divide and round to the nearest hundredth if necessary.

a) Prac Prob

b)

c)

5.2

Ex 28 Decide whether the answer is reasonable by using front-end rounding to estimate the answer. If the exact answer is not reasonable, find and correct the error.

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FLC Ex 29

Ch 5 Divide.

a)

b)

Ex 30

b)

(

d)

Simplify using the Order of Operations.

a)

d)

c)

)

(

)

(

e)

)

c)

(

f)

(

Ex 31

Given

)

and

)

, evaluate and simplify the following expression.

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FLC

Ch 5

Ex 32 (#108) A fungus called “white-nose syndrome” has killed an estimated 500,000 bats throughout the country. This means about 2,400,000 pounds of bugs aren’t eaten over the year, says Forest Service biologist Becky Ewing. How many pounds of insects does an average bat eat annually?

Sec 5.5: Fractions and Decimals

Writing a Fraction as an Equivalent Decimal (

)

Step 1: Divide the numerator of the fraction by the denominator. Step 2: If necessary, round the answer to the place indicated. Ex 33

Rewrite each fraction using long division notation.

a)

b)

Do not complete the division. c)

9

Ex 34

Write each fraction or mixed number as a decimal.

a)

Ex 35

b)

c)

d)

Write as decimals. Find the exact answer AND round to the nearest thousandth.

bar notation a)

e)

Intro to repeating

b)

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FLC

Ch 5

Terminating/Repeating Decimals First reduce the fraction to lowest terms. If the resulting denominator has a prime factorization of strictly consisting of 2’s and/or 5’s, the decimal will terminate. Otherwise, it will repeat and a repeating bar is necessary for exact answers.

Ex 36

Fill in the blank with

or . See number line on page 295.

a)

b)

c)

d)

e)

f)

g)

h)

i)

Ex 37

Arrange each group in order from smallest to largest.

a)

Ex 38 a)

b)

Convert each fraction to a terminating decimal. b)

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FLC Ex 39

Ch 5 Convert each fraction to a repeating decimal.

a)

Ex 40

b)

Simplify.

a)

b)

c)

d) PP

e) PP

f) PP

(

)

Summarize arithmetic rules of mixed numbers, fractions, and decimals.

Mixed Numbers

Fractions

Decimals

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FLC

Ch 5 Sec 5.7: Introduction to Square Roots

The Square of a Number Square Root Ex 41

If

, then

a)

Ex 43 a)

√

Ex 44

.

√

√

List all square roots of the given number. If the number has no square roots, write “none”. b)

c)

d)

e)

f)

Compute the square root. If the square root is undefined, write “und”. b)

c)

√

√

h)

√

is called the square of the number .

is called a square root of the number .

Find the square roots of 16. Next, find √

Radical Notation

Ex 42

The number

i)

√

d)

e)

√

√

f)

g)

√

√

j)

√

k)

√

√

Without using a calculator, estimate the square root to the nearest tenth. √

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FLC

Ch 5

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