Download SECTION 5.1 Decimals YouTube Video In Words

SECTION 5.1
Decimals
YouTube Video
123.456789
Give the place value and actual value of the 3 in the following:
a) 12.351
b) 1.43
c) 30.002
d) 0.123456
In Words
e) 52.543
f) 2.09
g) 2.009
h) Three hundred two and three thousandths
i) Four thousand and three hundredths
j) One hundred million, thirty-three thousand, five hundred eleven
k) Decimal to Fraction:
0.6 =
1.6 =
12.65 =
l) Write the following fractions/mixed numbers as decimals:
5
=
10
3
=
100
35
923
=
1000
Rounding to the nearest YouTube Video
Round to the nearest thousandth.
1) 234,123.5643
2) 0.2345
3) 1009.009
4) 1.2353363333
Round to the nearest hundredth
1) 234,123.5643
2) 0.2345
3) 1009.009
4) 1.2353363333
Round to the nearest whole number
1) 234,123.5643
2) 0.2345
3) 1009.009
4) 1.2353363333
Round to the nearest cent
1) $234,123.5643
2) $0.2345
3) $1009.009
4) $1.2353363333
Plot the following:
YouTube Video
Whole numbers: plot -2
Plot 5
Decimals:
plot -2.3
Plot 5.6
Fractions: plot 𝟒
𝟏
Plot −𝟑
𝟐
𝟏
𝟒
Linear Inequalities
, 
<,>
x4
Graph
Interval notation
1)
x2
Interval notation
2)
x6
Interval notation
x>-5
x<0
SECTION 5.2
Adding and Subtracting decimals YouTube Video
Add the following 10.25 and 1.356
Subtract 1.02 from 2
4.32-58.125
-4.32-58.123
Why do we line up the decimals:
+
1
+
3
4
Adding 17.6+2.35 represents the following:
17.6 is one 10, seven 1s, and 6/10
2.35 is
two 1s, and 3/10, along with 5/100
10 + 7 + 6/10
2 + 3/10 + 5/100
17.6
2.35
SECTION 5.3
MULTIPLICATION OF DECIMALS YouTube Video
1. Multiply
2. Count the number of decimal places in both numbers.
3. Give the product that number of decimal places.

0.04
0 .3
−12.5(0.1)
0.04(6)
Using repeated addition:
Jim makes a special sauce. He needs 0.2 ounces of hot sauce for each cup of water. If he uses 5 cups of water,
how many ounces of hot sauce does he need?
5(0.2) =
Why do we count the decimals:

0.04
0 .3
Power of 10
6500(10)
25(100)
YouTube Video
17(1000)
2.36 10
14.869 100
0.556 10,000
0.0056 10
2.33  100
0.55  100
2  10
0.25  1,000
SCIENTIFIC NOTATION
3,654,000,000,000
YouTube Video
0.000000000123
1) 32300000000
.
10
2) 2588800000000000
.
10
3) 56575
.
10
4) 0.000000000562
.
10
5) 0.789
.
10
6) 0.000000589
.
10
7) 56.8
8) 99999
9) 123.55
Scientific Notation to Decimal form
1) 3.15  10 6
2)
3.15 106
3)
9.35  105
4)
1.789 1015
5)
9  104
6)
3 10 -6
SECTION 5.4
DIVISION OF DECIMALS YouTube Video
1. If dividing by a decimal, then move the decimal place to the right in both numbers until there are no
decimal places on the outside number(the divisor).
2. Place a decimal on the line above the other decimal.
3. Divide as before until you have a remainder of zero, repeating digits, or it asks you to round. If the
digits repeat, then place a bar over the repeating digits.
1.3 3.328
.
13 33.28
The outside number had one decimal place. So we had to
move the decimal to the right one place in both numbers.
Divide 3 25
Why do we want the divisor to be a whole number?
Round to the nearest hundredth 13 200
SECTION 5.5
NATURAL NUMBERS (counting numbers)
1, 2, 3, 4, 5,…
YouTube Video
1 2 3 4 5 6 7 8 9 1
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …
WHOLE NUMBERS
0 1 2 3 4 5 6 7 8 9 10
INTEGERS…-3, -2, -1, 0, 1, 2, 3, …
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
RATIONAL NUMBERS Integers, Repeating and ending Decimals, and Fractions -3, -2
-5.5
0
7
, 0, 3, 5.7, 4.33333…
8
1
1
2
IRRATIONAL NUMBERS
Decimals that don’t repeat or end. We don’t know exactly where they are on the number line. Like radicals,
1.235698425624… there is no pattern.
REAL NUMBERS
,
All of the previous numbers
RATIONAL
INTEGERS
WHOLE NUMBERS
NATURAL
REAL
IRRATIONAL
So all natural numbers are whole numbers, all whole numbers are integers, all integers are rational, and all rational are real. The real
numbers are all the numbers on the real number line.
2,
3,  1, 0.5, 234.12, 0, 3, 
List all of the numbers that are:
1) whole numbers
2) Integers
3) Irrational
4) Rational
5) Real

Plot the following:
YouTube Video
Whole numbers: plot -2
Plot 5
Decimals:
plot -2.3
Plot 5.6
Fractions: plot 𝟒
𝟏
Plot −𝟑
𝟐
𝟏
𝟒
Linear Inequalities
, 
<,>
x4
Graph
Interval notation
1)
x2
Interval notation
2)
x6
Interval notation
x>-5
x<0
CONVERTING FRACTIONS TO DECIMALS
YouTube Video
Converting fractions to decimals (standard) :
3
5
2
7
8
35
2
3
2
11
Converting fractions to decimals (mentally) :
5
=
10
2
=
10
3
=
100
923
=
1000
9
10
21
=
100
7
3
5
7
8
CONVERTING DECIMALS TO FRACTIONS
YouTube Video
0.6 =
0.65 =
1.6 =
12.65 =
0.0006 =
Repeating decimals (basics):
̅
𝟏. 𝟒
0.654 =
123.654 =
1.0065 =
𝟐
𝟗
=
𝟐. ̅̅̅̅
𝟑𝟓
1000.004 =
𝟑𝟓
𝟗𝟗
𝟏𝟕𝟒
=
𝟗𝟗𝟗
̅̅̅̅̅̅
𝟎. 𝟓𝟔𝟕
=
𝟓𝟏
𝟗𝟗𝟗
𝟑𝟓
=
𝟗𝟗𝟎𝟎
̅̅̅̅̅̅
𝟎. 𝟎𝟎𝟓𝟔𝟕
=
SECTION 5.7
22 
SQUARE TO SQUARE ROOT YouTube Video
42
33 
9 3
44 
16  4
55 
25 
66 
36 
77 
49 
88 
64 
99 
81 
10 10 
100 
11 11 
121 
12 12 

 64
64
25
 0.64

25
64

9
81
 6 81  5 1
Approximate using your calculator:
√11
1
4
√52