Slide 1 / 183. Decimals
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1 Slide 1 / 183 Decimals
2 Slide 2 / 183 Table of Contents Define & Review Vocabulary Identify Place Values Read and Write Decimals Compare & Order Decimals Round Numbers to Designated Place Values Relate Fractions, Decimals & Percents Decimal Operations Real Life Applications
3 Slide 3 / 183 Define & Review Vocabulary Return to Table of Contents
4 Slide 4 / 183 What is a decimal number? Move me to find out! A Decimal Number (based on the number 10) contains a Decimal Point.
5 Slide 5 / 183 Yellow Rod How many yellow rods are needed to fill the blue block? What is the value of a yellow rod? Blue Block One Unit Red Block How many red blocks are needed to fill the blue block? (Hint: Fill a yellow rod with red blocks) What is the value of a red block?
6 Slide 6 / 183 Identify Place Values Return to Table of Contents
7 Slide 7 / 183 Place Value Chart million hundred thousand ten thousand thousand hundred ten one and tenth hundredth thousandth ten thousandth PULL NOTE: CAN BE STUDEN
8 Slide 8 / 183 million hundred thousand ten thousand thousand hundred ten one and tenth hundredth thousandth ten thousandth 9, 8 7 5, This number is read: Nine million, eight hundred seventy-five thousand, six hundred ten AND four thousand, seven hundred ninety-four ten thousandths Remember the place values after the decimal point start with tenths
9 Slide 9 / What digit is in the thousandths place? 4,567, A 7 B 1 C 3 D 8
10 Slide 10 / What digit is in the hundreds place? 6, A 7 B 4 C 3 D 0
11 Slide 11 / What digit is in the millionths place? 6,754, A 6 B 7 C 8 D 4
12 Slide 12 / What digit is in the tens place? 5, A 4 B 1 C 9 D 3
13 Slide 13 / What digit is in the ten thousands place? 543, A 3 B 4 C 2 D 5
14 Slide 14 / 183 Can you read the number? thousands hundreds tens ones and tenths hundredths thousandths
15 Slide 15 / 183 Read & Write Decimals Return to Table of Contents
16 Slide 16 / Look to see if there is a number to the left of the decimal; if so write it out. If there is no number to the left of the decimal, skip to step Write an and for the decimal point. 3. Write the number in the decimal part. 4. Write the word for the place value of the rightmost digit. How do you write a decimal in words? Write in words Thirteen and twenty-four hundredths
17 Slide 17 / 183 How does a comma help when writing a decimal number? The place value before the comma is always stated. For example: 1,547 is written One THOUSAND, five hundred forty-seven 6,547,100 is written 6 MILLION, five hundred forty-seven THOUSAND, one hundred
18 Slide 18 / 183 Write the decimal in words 1) 5.04 Five and four hundredths 2) One hundred forty-six and four hundred fifty-seven thousandths 3).0009 Nine ten-thousandths 4) 6, Six thousand, three hundred forty-five and one thousand, four hundred ninety-eight ten thousandths
19 Slide 19 / 183 Writing a decimal numerically 1. If there is a ths, there will be a decimal 2. If there is an and, there will be a whole number to the left of the decimal 3. Note the ending - this is the place where the decimal number will end 4. Use the decimal chart to help you!
20 Slide 20 / 183 Use the chart as a guide to write the decimal numbers thousands hundreds tens ones and tenths hundredths thousandths 1. four hundred nineteen and five hundredths 2. sixty-five and nine thousandths 3. seven thousand, four hundred thirty-three and twenty hundredths 4. six thousand and eight tenths
21 Slide 21 / 183 Compare & Order Decimals Return to Table of Contents
22 Slide 22 / 183 Comparing Decimals Line up all of the decimal points Put zeros in wherever digits are missing Compare the digits, from left to right The largest digit, having the same place value, names the largest number Example: Why is this the smallest number? What digit tells us this is the largest number? 1 Compare the digits
23 Order from least to the greatest Slide 23 / 183
24 Slide 24 / 183 Order from least to greatest
25 Slide 25 / The number with the least value is: A B C D
26 Slide 26 / The number with the least value is: A 0.01 B C D
27 Slide 27 / The number with the greatest value is: A 2.9 B 2.99 C D
28 Slide 28 / The number with the greatest value is: A B C D
29 Slide 29 / How much money would you like to win? A B C D
30 Slide 30 / 183 Round Numbers to Designated Place Values Return to Table of Contents
31 Slide 31 / 183 Rounding De cimals Let's learn how to round decimals using the following examples: Round to the nearest tenths place. When rounding decimals, put your pencil point under the place value that you are rounding to DO NOT MOVE IT
32 Slide 32 / 183 Put your pencil point under the digit in the tenths place Look to the right. Is the digit 5 or more? Yes OR No What happens to the 2? Increases by 1 OR remains the same What happens to everything to the left of the tenths place? Those digits always remain the same. Final Answer: 513.3
33 Slide 33 / 183 What happened to the digits to the right of the tenths place? Remember, we are rounding. The place values to the right of the tenths place have zero value, so now the digits 8 and 7 become zeroes = Try the next example...
34 Slide 34 / 183 Round to the nearest hundredths place. First, choose the digit that represents the hundredths place A B C D Choose which letter is under the hundredths place. First, put your pencil point under the 4 and look at the digit to the right. Ask yourself: "Is this digit 5 or more?" Since it's a 1, the 4 remains a 4, and everything after it becomes a zero = Answer?
35 Slide 35 / 183 Caution! When rounding to a specific place, your answer MUST have a digit in that place. Example: Round to the nearest tenth Answer: 15.0 There must be a digit in the tenths place, since we were to round to the tenths place. Try this: Round to the nearest hundredths place Answer:
36 Slide 36 / Round to the nearest hundredths
37 Slide 37 / Round to the nearest hundred
38 Slide 38 / Round to the nearest tenths
39 Slide 39 / Round to the nearest thousandths
40 Slide 40 / Round to the nearest unit
41 Slide 41 / 183 Relate Fractions, Decimals & Percents Return to Table of Contents
42 decimals Slide 42 / 183 Writing Decimals as Fractions fractions
43 Slide 43 / 183 Writing decimals as fractions... Example 1: 0.25 = Move the decimal part of the original number into the numerator (without the decimal point)
44 Slide 44 / 183 Writing decimals as fractions... Example 1: 0.25 = Then count the number of places to the right of the decimal point. This place value will become your denominator...
45 Slide 45 / 183 Writing decimals as fractions... Example 1: 0.25 = = 1 4 Finally, simplify the fraction.
46 Slide 46 / 183 Writing decimals as fractions... Example 2: = Move the decimal part of the original number into the numerator (without the decimal point)
47 Slide 47 / 183 Writing decimals as fractions... Example 2: = 32 1,000 Then count the number of places to the right of the decimal point. This place value will become your denominator...
48 Slide 48 / 183 Writing decimals as fractions... Example 2: = = Finally, simplify the fraction.
49 Slide 49 / 183 Writing decimals as fractions... Example 3: 4.1 = If there is a whole part to the original number, move the whole part to front of the fraction. Move the decimal part of the original number into the numerator (without the decimal point) What will the place value be?
50 Slide 50 / 183 Writing decimals as fractions... Example 3: 4.1 = Can this fraction be reduced?
51 Slide 51 / 183 Let's review how to write a decimal as a fraction! Numerator is decimal part of the original number Denominator is place value of rightmost digit Simplify the fraction Whole numbers are written in front of the fraction
52 Slide 52 / Write the decimal as a fraction or mixed number in simplest form: 0.85
53 Slide 53 / Write the decimal as a fraction or mixed number in simplest form: 4.375
54 Slide 54 / Write the decimal as a fraction or mixed number in simplest form:
55 Slide 55 / Write the decimal as a fraction or mixed number in simplest form: 14.12
56 Slide 56 / Write the decimal as a fraction or mixed number in simplest form: 8.002
57 Slide 57 / 183 Common Equivalents you should know like the back of your hand!
58 Slide 58 / 183 Some repeating decimals can be converted to fractions. These are common equivalents you should also know!
59 decimals Slide 59 / 183 Writing Fractions as Decimals fractions
60 Slide 60 / 183 Writing fractions as decimals... Example 1: 7 20 = 7 20 The Pit! Divide the numerator by the denominator... Or kick the numerator into the pit!
61 Slide 61 / 183 Writing fractions as decimals... Example 1: 7 20 = = 0.35 Then do the math
62 Slide 62 / 183 Writing fractions as decimals... Example 2: = The Pit! Divide the numerator by the denominator... Or kick the numerator into the pit! PULL It is less work to put the 3 in front of the decimal point. What happens if we change the mixed number to an improper fraction? Do we eventually get the same answer?
63 Slide 63 / 183 Writing fractions as decimals... Example 2: = 3 = Then do the math What happens if you use 29 8?
64 Slide 64 / 183 Writing fractions as decimals... Example 3: 5 6 = 5 6 The Pit! Divide the numerator by the denominator... Or kick the numerator into the pit!
65 Slide 65 / 183 Writing fractions as decimals... Example 3: 5 6 = = 0.83 Then do the math
66 Definitions: Slide 66 / 183 Repeating decimal: A decimal in which a pattern of one or more digits is repeated indefinitely, such as To show that a decimal is repeating, a bar is often put above the repeating digits:.35 means A repeating decimal does not end. Terminating decimal: A decimal that has only a finite number of nonzero digits to the right of the decimal point, such as 0.56 Challenge Create a decimal that is non-terminating and non-repeating.
67 Slide 67 / 183 Writing fractions as decimals... Example 4: 5 3 = 5 3 The Pit! Divide the numerator by the denominator... Or kick the numerator into the pit!
68 Slide 68 / 183 Writing fractions as decimals... Example 4: Repeating 5 3 = = 1.6 decimal! Then do the math
69 Slide 69 / 183 Writing fractions as decimals... Example 5: -7 4 = = Then do the math
70 Slide 70 / Write the fraction as a decimal: 3 10
71 Slide 71 / Write the mixed number as a decimal: 3 4 5
72 Slide 72 / Write the fraction as a decimal: 31 22
73 Slide 73 / Write the fraction as a decimal and round to the nearest hundredth: 3 7
74 Slide 74 / Write the fraction as a decimal: -12 5
75 Slide 75 / 183 Common Equivalents you should know like the back of your hand!
76 Slide 76 / 183 Common Equivalents you should know like the back of your hand!
77 0 Slide 77 / 183 Writing Decimals as Percents de cimals percents
78 Slide 78 / 183 What does percent mean? Percent means parts per 100 The symbol is % Example: 50% means 50 per 100
79 Slide 79 / 183 Writing decimals as percents... Multiply by 100 and add the percent symbol. Example 1: 0.75 = = % 100 Remember To multiply a # by 100, move the decimal two places to the RIGHT. 0.75
80 Slide 80 / 183 Writing decimals as percents... Multiply by 100 and add the percent symbol. Example 2: 0.09 = = % 100 Remember To multiply a # by 100, move the decimal two places to the RIGHT. 0.09
81 Slide 81 / 183 Writing decimals as percents... Multiply by 100 and add the percent symbol. Example 3: = = 0.7% Remember To multiply a # by 100, move the decimal two places to the RIGHT
82 Slide 82 / 183 Writing decimals as percents... Multiply by 100 and add the percent symbol. Example 4: 0.4 = = % 100 Remember To multiply a # by 100, move the decimal two places to the RIGHT. 0.4
83 Slide 83 / 183 Writing decimals as percents... Multiply by 100 and add the percent symbol. Example 5: 1.49 = = % 100 Remember To multiply a # by 100, move the decimal two places to the RIGHT. 1.49
84 Slide 84 / 183 Writing decimals as percents... Multiply by 100 and add the percent symbol. Example 6: 8 = = 800% Remember To multiply a # by 100, move the decimal two places to the RIGHT. 8
85 Slide 85 / Write the decimal as a percent: %
86 Slide 86 / Write the decimal as a percent: %
87 Slide 87 / Write the decimal as a percent: %
88 Slide 88 / Write the decimal as a percent: 5 500%
89 Slide 89 / Write the decimal as a percent:.2 20%
90 Slide 90 / 183 Writing Percents as Decimals percent de cimal
91 Slide 91 / 183 Writing percents as decimals... Divide by 100 and remove the percent symbol. Example 1: 28% = = 28% Remember To divide a # by 100, move the decimal two places to the LEFT. 28%
92 Slide 92 / 183 Writing percents as decimals... Divide by 100 and remove the percent symbol. Example 2: 8% = = 8% Remember To divide a # by 100, move the decimal two places to the LEFT. 8%
93 Slide 93 / 183 Writing percents as decimals... Divide by 100 and remove the percent symbol. Example 3: 0.4% = = 0.4% Remember To divide a # by 100, move the decimal two places to the LEFT. 0.4%
94 Slide 94 / 183 Writing percents as decimals... Divide by 100 and remove the percent symbol. Example 4: 375% = 375% 100 = 3.75 Remember To divide a # by 100, move the decimal two places to the LEFT. 375%
95 Slide 95 / Write the percent as a decimal: 2%.02
96 Slide 96 / Write the percent as a decimal: 658% 6.58
97 Slide 97 / Write the percent as a decimal: 0.019%.00019
98 Slide 98 / Write the percent as a decimal: 4.3%.043
99 Slide 99 / Write the percent as a decimal:.5% 0.005
100 Slide 100 / 183 Writing Fractions as Percents percents fractions
101 Slide 101 / 183 Writing fractions as percents... Write an equivalent fraction with a denominator of 100. Example 1: 3 4 = x x = %
102 Slide 102 / 183 Writing fractions as percents... Write an equivalent fraction with a denominator of 100. Example 2: 4 5 = x x = %
103 Slide 103 / 183 Writing fractions as percents... Write an equivalent fraction with a denominator of 100. Example3: 9 4 = x x = %
104 Slide 104 / 183 Writing fractions as percents... Write an equivalent fraction with a denominator of 100. Example 4: x 3 = = x %
105 Slide 105 / Write the fraction as a percent: %
106 Slide 106 / Write the fraction as a percent: %
107 Slide 107 / Write the fraction as a percent: %
108 Slide 108 / Write the fraction as a percent: %
109 Slide 109 / Write the fraction as a percent: %
110 Slide 110 / 183 To write any fraction as a percent: Express the fraction as a decimal and then express the decimal as a percent. Example 5: %
111 Slide 111 / 183 To write any fraction as a percent: Express the fraction as a decimal and then express the decimal as a percent. Example 6: %
112 Slide 112 / 183 To write any fraction as a percent: Express the fraction as a decimal and then express the decimal as a percent. Example 7: %
113 Slide 113 / Write the fraction as a percent: %
114 Slide 114 / Write the fraction as a percent. Round to the nearest whole percent %
115 Slide 115 / Write the fraction as a percent: %
116 Slide 116 / Write the fraction as a percent: %
117 Slide 117 / Write the fraction as a percent: %
118 Slide 118 / 183 Writing Percents as Fractions percents fractions
119 Slide 119 / 183 Writing percents as fractions... Express the % as a fraction with a denominator of 100, then simplify. Example 1: 75% = = 3 4
120 Slide 120 / 183 Writing percents as fractions... Express the % as a fraction with a denominator of 100, then simplify. Example 2: 120% = = 1 1 5
121 Slide 121 / 183 Writing percents as fractions... Express the % as a fraction with a denominator of 100, then simplify. Example 3: 0.3% = = Multiply by 10 to get rid of the decimal
122 Slide 122 / 183 Writing percents as fractions... Express the % as a fraction with a denominator of 100, then simplify. Example 4: % = 4 = = ,000 = Multiply by 100 to get rid of the decimal
123 Slide 123 / 183 Writing percents as fractions...another way Express the % as a fraction with a denominator of 100, then simplify. Example 4: Convert the percent to a fraction. Divide the numerator by the denominator (100). Simplify.
124 Slide 124 / Write the percent as a fraction in simplest form: 40% 2 5
125 Slide 125 / Write the percent as a fraction in simplest form: 110% 11 10
126 Slide 126 / Write the percent as a fraction in simplest form: 0.5% 1 200
127 Slide 127 / Write the percent as a fraction in simplest form: 8% 2 25
128 Slide 128 / Write the percent as a fraction in simplest form: 1 5 %
129 Slide 129 / 183 Relate Fractions, Decimals & Percents...Tying it all together!
130 Slide 130 / 183 Helping you remember... Fill in each box below with an example of the process described. % to a fraction % to a decimal fraction to a % decimal to a %
131 Slide 131 / Find the lowest value A 5% B 1/2 C.5% D.05
132 Slide 132 / Find the greatest value A 120% B 1.02 C.2% D 1.19
133 Slide 133 / Find the greatest value A 6% B.6 C 60 D 6
134 Slide 134 / Find the lowest value A 2% B.2 C.02 D.2%
135 Slide 135 / Find the lowest value A 50% B 500% C 50.0 D 50.01
136 Slide 136 / 183 Reorder the amount starting with the lowest value
137 Slide 137 / 183 Reorder the amount starting with the lowest value
138 Slide 138 / 183 Reorder the amount starting with the lowest value
139 Slide 139 / 183 Decimal Operations Return to Table of Contents
140 Slide 140 / 183 Add decimals Four quarters equal one dollar = $1.00
141 Slide 141 / 183 When adding or subtracting decimals, always remember to align the decimals vertically
142 Slide 142 / 183 Now, try this - Don't forget - LINE 'EM UP
143 Slide 143 / 183 If you know how to add whole numbers then you can add decimals. Just follow these few steps. Step 1: Put the numbers in a vertical column, aligning the decimal points. Step 2: Add each column of digits, starting on the right and working left. Step 3: Place the decimal point in the answer directly below the decimal points that you lined up in Step 1.
144 Slide 144 / Add the following: A 6.1 B C 1.15 D 0.16
145 Slide 145 / Find the sum
146 Slide 146 / What is the sum of and ? A B B C D
147 Slide 147 / Find the sum A B C D 20.14
148 Slide 148 / Find the sum:
149 Slide 149 / 183 Let's go to Cool Math and practice addition: Cool Math Link
150 Slide 150 / 183 Subtract decimals Put the numbers in a vertical column aligning the decimal points Subtract the numbers from right to left using the same rules as whole numbers
151 Slide 151 / 183 What do we do if there aren't enough decimal places when we subtract? Don't forget...line 'em Up! What goes here?
152 Slide 152 / 183 Let's go to Cool Math and practice subtraction: Cool Math Link
153 Slide 153 /
154 Slide 154 /
155 Slide 155 /
156 Slide 156 /
157 Slide 157 /
158 Slide 158 / 183 Multiply & Divide Decimals To multiply two decimals: Ignore the decimal points Multiply the numbers Count the total number of digits to the right of the decimal points Put that many digits to the right of the decimal point in your answer
159 Slide 159 / 183 Multiply & Divide Decimals 3.21 x.04 }.1284 There are a total of four digits to the right of the decimal points. There must be four digits to the right of the decimal point in the answer.
160 Slide 160 / x } There are a total of three digits to the right of the decimal points. There must be three digits to the right of the decimal point in the answer.
161 67 Multiply 0.4 x 0.03 Slide 161 / 183
162 68 Multiply 3.45 x 2.1 Slide 162 / 183
163 69 Multiply 53 x 0.08 Slide 163 / 183
164 70 Multiply 4.01 x 7.8 Slide 164 / 183
165 71 Multiply x 0.21 Slide 165 / 183
166 Slide 166 / 183 Divide decimals To divide a decimal by a whole number: Use long division. Bring the decimal point up in the answer
167 Slide 167 / 183 Try these! PULL Pull
168 Slide 168 / 183 To divide a number by a decimal: Change the divisor to a whole number by multiplying by a power of 10 Multiply the dividend by the same power of 10 Divide Bring the decimal point up in the answer Divisor Dividend
169 Slide 169 / Multiply by 10, so that 15.6 becomes must also be multiplied by Multiply by 1000, so that.234 becomes must also be multiplied by 1000
170 Slide 170 / 183 By what power of 10 should the divisor and dividend be multiplied? means means
171 Slide 171 / Divide
172 Slide 172 /
173 Slide 173 / divided by 0.25
174 Slide 174 /
175 Slide 175 /
176 Slide 176 / 183 Real Life Applications Return to Table of Contents
177 Slide 177 / If you had six hundredths of a mile left to run, how would you write this distance as a decimal? A 6.0 Pull B.6 C.06 D 06.0 C E.60
178 Slide 178 / Your weekly grocery bill averages $ Round your total to the nearest 10 dollars to figure out approximately how much money to save for groceries per week. A $ B $90.00 C $97.00 A D $95.00
179 Slide 179 / Sally won $25.00 for her science fair project. Her project cost $12.57 to prepare. How much did Sally actually make as a profit? A $37.57 B $12.43 C $13.57 D $12.00 B
180 Slide 180 / Five students collected paper to be recycled. Shelly's stack was.008 cm. thick; Ken's stack was.125 cm. thick; Joe's stack was.150 cm. thick; Betty's stack was.185 cm. thick; Mary's stack was.005 cm. thick. What was the thickness of the papers collected to be recycled? A B C D.561 cm..452 cm..480 cm..473 cm. D
181 Slide 181 / The regular price of a pair of jeans is $ Mrs. Jones has four children for whom she must buy new jeans. The jeans are on sale for $ What would the total cost be of four pairs of jeans on sale? A $ B $90.00 C $86.00 B D $52.49
182 Slide 182 / The regular price of a pair of jeans is $ Mrs. Jones has four children for whom she must buy new jeans. The jeans are on sale for $ How much money does she save by buying the jeans on sale? A $7.49 B $30.96 C $29.96 C D $89.96
183 Slide 183 / 183
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