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