Math 009

Unit 4

Lesson 1

Obj: To write decimals in words

tent

hshu

ndre

dths

thou

sand

ths

a

nd

ten-

thou

sand

ths

on

es

te

ns

h

undr

eds

15.157

1 5 1 5 7

Fifteen and one hundred fifty-seven thousandths

Obj: To write decimals in words

tent

hshu

ndre

dths

thou

sand

ths

a

nd

ten-

thou

sand

ths

on

es

te

ns

h

undr

eds

306.0017

0 6 0 0 1

Three hundred six and seventeen ten-thousandths

3 7

Obj: To write words as decimals

tent

hshu

ndre

dths

thou

sand

ths

a

nd

ten-

thou

sand

ths

on

es

te

ns

h

undr

eds

5.38

5 3 8

Five and thirty-eight hundredths

Answer:

Obj: To write words as decimals

tent

hshu

ndre

dths

thou

sand

ths

a

nd

ten-

thou

sand

ths

on

es

te

ns

h

undr

eds

19.004

9 0 0

Nineteen and four thousandths

Answer:

1 4

Obj: To write words as decimals

tent

hshu

ndre

dths

thou

sand

ths

a

nd

ten-

thou

sand

ths

on

es

te

ns

h

undr

eds

0.0071

0 0 0

Seventy-one ten-thousandths

Answer:

17

Naming place values:

Name the place value of the digit 7

56.03789

263.893475

46.759834

thousandths

hundred-thousandths

tenths

Ordering decimal numbers

Place the correct symbol between the two numbers

7.6005 7.605 Line up the decimals

7.6005

7.605

<

Write the following numbers in order from smallest to largest

0.24, 0.024, 0.204, 0.0024 0.24

0.024

0.204

0.0024Answer:

0.0024, 0.024,0.24

0.204

0.024

0.0024

0.204, 0.24

Obj: To round a decimal to a given place value.

Round 4.349254 to the nearest hundredth

4.349254

Round 4.349254 to the nearest ten-thousandth

4.3493

4.35

4.349254

Obj: To round a decimal to a given place value.

Round 4.349254 to the nearest tenth

Round 15.0538 to the nearest hundredth

Round 15.0538 to the nearest tenth

4.349254

4.3

15.0538

15.05

15.0538

15.1

Operations on

decimals

Obj: To add decimals without a calculator

• Write the numbers so that the decimals points are on a vertical line• add the columns just as you would with whole

numbers

Example: Find the sum of 42.3, 65.0729 and 162.903

42.3 65.0729 162.903 +

111

Answer: 270.2759

959759.27590.275970.2759270.2759

Obj: To subtract decimals without a calculator

• Write the numbers so that the decimals points are on a vertical line• subtract the columns just as you would with whole numbers

Example: Subtract 39.047 and 7.96

39.0477.96 –

14

270.2757270.2787

98

Answer: 31.087

270.087231.087231.087

Find the following sums or differences

1. -31.894 + 7.5

2. -1.09 – (-8.3)

3. -5.6 – (-3.82) – 17.409

4. How much greater is -31 than -62.09 ?

= -24.394

= -1.09 + 8.3 = 9.39

= -5.6 + 3.82 – 17.409

= -19.189

-31 – (-62.09) = 31.09= -31 + 62.09

Obj: To solve application problems involving decimals

Find the missing length on the shaft

2.77 cm ? 3.2 cm

Solution: 2.77 + 3.2 = 5.97

missing length = 2.63 cm

8.6 cm

missing length = 8.6 – 5.97

Obj: To solve application problems involving decimals

Grace owned 357.448 shares of a mutual fund on January 1. On December 31 of the same year she noticed that her shares had increased by 82.469 shares. What was her new total at the end of that year?

Solution: New Total = 357.448 + 82.469

= 439.917 shares

Estimate by rounding; then find the exact answer

6.272 – 1.848

Estimation: 6 – 2 = 4

Exact answer:

Evaluate x – y when x = 6.029 and y = - 4.708

x – y = 6.029 – (-4.708)

= 6.029 + 4.708

= 10.737

6.272 – 1.848 = 4.424

Obj: To multiply decimals without a calculator

• multiply the numbers as if they were whole numbers

• the number of decimal places in the answer is the sum of the decimal places in the factors

Multiply: 0.000086 x 0.057

0.000086 0.057x

602 430

4902

Total decimal places in the factors is 9

Total decimal places in the answer is 9 ^

Answer: 0.000004902

00000

Obj: To divide decimals without a calculator

7.06 420.9^ ^

706

5

35306790

6

6354436 0

9

423 612 4

Answer

Divide: 420.9 7.06Round your answer to the nearest tenth

042090. 00

0

1

7 06

59.6

Do the following multiplications and divisions

(0.72)(-3.7)

-5.2(-0.8)

-0.074 (10,000)

27.08 (-0.4)

58.37 1000

= - 2.664

= 4.16

= - 740

= - 67.7

= 0.05837

Do the following multiplications and divisions

Round answers to the nearest hundredth

(5.78)(-3.799)

-(18.47)(2.003)

8.57 0.949

27.08 (-3.14)

21.96

- 37.00

9.03

-8.62

= 21.95822

= -36.99541

= 9.030558483

= -8.624203822

Obj: To multiply decimals by powers of 10

• move the decimal point to the right the same number of places as the number of zeros in the power of 10

Multiply: 0.4207 x 1000

^.4207 x 1000 = 4207 = 420.7

Multiply: 63.75 x 10,000

^63.75 x 10,000 = 6375 = 637,50000

Obj: To multiply decimals by powers of 10

• move the decimal point to the right the same number of places as the power of 10

Multiply: 0.00006835 x 103

^.00006835 x 103 = 00006835 = 0.06835

Multiply: 4.68 x 105

^4.68 x 105 = 468 = 468,000 000

• if the power of 10 is written in exponent form

Obj: To divide decimals by powers of 10

Divide: 58.3 103

^58.3 103 = 0583 = 0.0583

Divide: 0.625 100

^0.625 100 = 00625 = 0.00625

• move the decimal in the dividend to the left the same number of places as the power of 10 (same number of places as the number of zeros)

Obj: To convert fractions to decimals• divide the numerator by the denominator

• round the decimal answer if necessary

Convert to a decimal:

3 8

• place a bar over repeating digits

17 258

1 64

= 0.375

= 8.68

= 4.1666… = 4.16

Obj: To convert fractions to decimals

Certain conversions from fractions to decimals should be memorized

14 = 0.25

12 = 0.5

34 = 0.75

13 = 0.333… = 0.3

23 = 0.666… = 0.6

Obj: Convert decimals to fractions• remove the decimal point

• for a denominator use a power of ten that corresponds to the decimal places in the original number

• reduce the fraction

Convert fractions

0.35 =35100

= 720

0.275 =2751000

= 1140

5.76 = 76 1005 = 19

255

Obj: Compare a decimal and a fraction• change the fraction to a decimal

• compare the decimals

Place the correct symbol, > or <, between the numbers

3 80.32 < 44.509

4.5094.5

> 12

00

0.32 0.375 4.509 4.5

0.320.375

Checking a solution to an equation

Is -1.2 a solution for 6.4 = 5.2 + x ?

6.4 = 5.2 + x

6.4 5.2 + (-1.2)

4

No , -1.2 is not a solution for the equation

Checking a solution to an equation

Is -3.6 a solution for -9x = 32.4 ?

-9x = 32.4

-9(-3.6) 32.4

Yes , -3.6 is a solution for the equation

32.4