unit two - operations with decimals · 9.09 5.045. december 10, 2015 drag the numbers to the right...
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December 10, 2015
Unit Two - Operations with decimals
December 10, 2015
Unit Two - Operations with Decimals
Place Value
Introduction (or re-introduction) to place value
Read the following numbers (properly!)
145
2.35
1 567 043.793
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ones
1
tens
10
hund
reds
100
tent
hs
0.1
hund
redt
hs
0.01
thou
sand
ths
0.001
thou
sand
s1000
ten-
thou
sand
s
10,000
ten-
thou
sand
ths
0.0001
hund
red
thou
sand
s
100,000
mill
ions
1,000,000 Place Value
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Place Value
The value of a digit is based on its place in a number. This is known as its place value.
Place Value Chart
thousandths
ten thousandths
hundred thousandths
millions
decimal point
ones
tenths
hundredths
tenths
hundredths
thousandths
ten thousandths1,356,426.7142 Ex
ampl
e
The place value of the digit 6 in the number 1234.5679 is hundredths.
Teac
her's
Not
es
1. Explain the concept of place value of a digit in a number.
2. Explain the place value of each digit in the given place value chart.3. Cite some more examples for the students to practice.
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3.085 →
1,085.06 →
To write a number in expanded notation, take each digit times its place-value, then add the pieces together. For zeros in the number, just skip over those place
values, you don’t need to write them.
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Write the number in expanded notation
12.25
308.4
2400.0542 x 1000 + 4 x 100 + 5 x 0.01 + 4 x 0.001
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Write the number in standard form.(3 x 1) + (2 x 0.1) + (2 x 0.01)
(4 x 100) + (1 x 1) + (6 x 0.001) + (3 x 0.0001)
(6 x 10) + (7 x 1) + (3 x 0.1) + (9 x 0.001)
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Standard Form ↔ WordsTo write a number in words:• say the whole number part• say AND in place of the decimal• say the decimal part, finishing with the place value where the number ends.
13.28 ⇒
0.405 ⇒
3.007 ⇒
Click to hear number said in words.
9.075 ⇒
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Going from words to standard (number) form:
Ex: Three hundred sixteen and fifteen thousandths
316.015
Tells you where the decimal part ends
thirty-four and sixteen hundredths
one hundred twenty-two thousandths
eleven and three hundredths
34.160.122
11.03
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Match the number in standard form and in words.
1
6
5
4
3
2
Click on a number to hear it said in words.
31850.45
0.318
0.9099.09
5.045
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Drag the numbers to the right to reveal the number in words.
44.04 forty-four and four hundredths
4.404 four and four hundred four thousandths
440.4 four hundred forty and four tenths
0.46 forty-six hundredths
0.046 forty-six thousandths
4.6 four and six tenths
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Round off to Number of Digits
Round off the number 56.782398 to three decimal places.
5 6 . 7 8 2 3 9 8
Teac
her's
Not
es
1. Explain the reasons to round off decimal numbers. We round off decimal numbers to: Avoid repetitive decimals. Make it easy to calculate. Delete the irrelevant number of digits (For example, third decimal digit has little value in amounts expressed in dollars).
2. Explain how to round off values to a specified number of places.3. Ask a student to count three decimal digits and circle the fourth digit.4. Call another student to check if the circled digit is more than or equal to 5. If so, tell him or her to add one to the third decimal digit to get the correct answer as 56.7825. Cite more examples for the students to practice.
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Activity
Write the correct round off values of pi (3.1415927) to the specified number of digits.
0 decimal digits
1 decimal digit2 decimal digits
3 decimal digits
4 decimal digits5 decimal digits
6 decimal digits
Cor
rect
Ans
wer
Teac
her's
Not
es
1. Call six students one-by-one to write the value of pi to the number of decimal digits in each column.2. Congratulate the students who write the correct answers.3. Pull the Correct Answer box, if required.4. You may try the same activity with other decimal numbers too.
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Select the correct answer.
Check Your Understanding
1 Round off the number 384.225 to two decimal points.
A 384.20
B 384.22
C 384.23
D 384.25
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Round off to Place Values
In the year 2009, the population of the state of New York stood at 19,541,453.Round off the population to its nearest thousands.
1 9 , 5 4 1 , 4 5 3Teac
her's
Not
es
1. Explain how to round off values to the nearest place value.2. Ask a student to circle the digit in the hundreds place.3. Call another student to check if the circled number is more than or equal to 5. 4. If so, tell him or her to add one to the digit in the thousands place and rewrite the other digits on the right side as zeroes to get the correct answer as 19,541,000.5. Cite more examples for the students to practice.
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Activity
Round off the number 78956.34854 to:
Thousands
HundredsTens
Ones
TenthsHundredths
Thousandths
Cor
rect
Ans
wer
Teac
her's
Not
es
1. Call seven students one-by-one to write the round off value nearest to the given place value.2. Congratulate the students who write the correct answers.3. You may try the same activity with other decimal numbers too.
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Estimating with Decimals
Why would we need to estimate?
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0.0167 0.015 0.0105 0.018 0.013
Place the decimals on the number line
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Which of the decimals round to 0.02?
0.01670.0105
0.0180.013 0.015
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0.009
0.009 0.010 0.011
Place the decimals on the number line
0.00950.009450.0104 0.0107
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0.009
0.009 0.010 0.011
Which of the decimals round to 0.01?
0.0095
0.00945
0.0104
0.0107
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20
100
50
0.9
0.003
101.34
53.973
0.9234
0.0027
17.6
Round to the highest place value
?
?
?
?
?highest place value
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25.89 + 12.27 + 9.704
0.043 + 0.057 + 0.099
0.00095 + 0.578 + 0.063
+ + =
+ + =
+ + =
Use rounding to estimate these sums
30 + 10 + 10 = 50
0.04 + 0.06 + 0.1 = 0.2
0.001 + 0.6 + 0.06 = 0.661
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86.89 - 9.532
0.894 - 0.25
0.078 - 0.021 - 0.0099
- =
- - =
- =
Use rounding to estimate differences
90 - 10 = 80
0.9 - 0.3 = 0.6
0.08 - 0.02 - 0.01 = 0.05
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Homework
Complete the Estimating side of the worksheet
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Adding and Subtracting Decimals
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How to Add and Subtract Decimals:
Adding Decimals
The key is to line up all the decimal points in a vertical line.
Subtracting Decimals
45.123.71_____+
48.83
48.183.01
45.17
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Adding Decimals
10.3427.5645.33+
10 + 27 + 45 = 70 + 12 = 820.34 + 0.56 + 0.33 = 1.1 + 0.13 = 1.23 82 + 1.23 = 83.23
9.0816.99+
9 + 16 = 250.99 + 0.08 = 1.0725 + 1.07 = 26.07
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9.09
8.32
8.7
9.53
What was Courtney's total score?
How much more did she score on the beam than the floor?
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December 10, 2015
Homework
p 48-51Complete any 10 questions (1 a.b.c counts as one question)
Worksheet - adding and subtracting decimals
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Working with powers of tenMultiplying Decimals
1 000 000100 00010 0001 0001001010.10.010.0010.00010.0001
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Review: Multiplying Whole Numbers by 1, 10, 100, and 1,000.
36 x 1 =
36 x 10 =
36 x 100 =
36 x 1,000 =
36
360
3,600
36,000
2 x 1 = 2
2 x 10 = 20
2 x 100 = 200
2 x 1,000 = 2,000
Click on each black dot to reveal answers to the problems in the second column.
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Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000.
0.0007 x 1 =
0.0007 x 1,000 =
0.0007 x 10 =
0.0007 x 100 =
0.007
0.07
0.7 The decimal point moves 3 places to the right.0.71 2 3
The decimal point moves 2 places to the right.0.071 2
The decimal point moves 1 place to the right.0.0071
0.00070.0007 The decimal point stays in the same place.
Click on each problem's answer to see the pattern.
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Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000.
0.521 x 1 =
Click on each black dot to reveal the answer for the problems.
0.521 x 1,000 =
0.521 x 100 =
0.521 x 10 =
0.521
5.21
52.1
521
The decimal point stays in the same place.
The decimal point moves right 1 place.
The decimal point moves right 2 places.
The decimal point moves right 3 places.
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Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000.
0 0 0 0 2 x 10Help Deci the Frog jump the correct number of lily pads and reveal the answer!
0.002Answer
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Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000.
0 3 2 x 100Help Deci the Frog jump the correct number of lily pads and reveal the answer!
32Answer
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Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000.
3 0 1 6 8 x 1000Help Deci the Frog jump the correct number of lily pads and reveal the answer!
3,016.8Answer
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Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000.
3.5 x 1 =
3.5 x 1,000 =
3.5 x 100 =
3.5 x 10 =
3.5
35
350
3,500
The decimal point stays in the same place.
The decimal point moves right 1 place.
1 zero must be added as a place holder.
2 zeroes must be added as place holders.
Sometimes you must add zeroes to the end as place holders!
00
0
Click on each black dot to reveal the answer for the problems.
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Answer
70,160
0 7 0 1 6 x 1000Draw Deci's path and then move Deci to the lily pad to check your answer.
Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000.
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Answer
0
40
0 4 x 100Draw Deci's path and then move Deci to the lily pad to check your answer.
Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000.
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Move the decimal point to the correct postion and then click on Deci to check your answer!
Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000.
0.542 X 10 = 0 5 4 2
$6.75 x 100 = $6 7 5
You may need to add zeroes as placeholders.
1000 x 0.5 = 0 5
5.42
$675
500
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Decimals
Continue the pattern with decimal powers of ten.
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Multiplying Decimals
Use estimation to help determine if your answers are correct.
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0.8
x
X 0.2
=
= n
Modeling Decimal Multiplicationexample
What decimal represents the part of the whole that is orange?
0.16Click herefor theanswer
Click herefor theanswer
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0.28
22 0.6 x 0.5 =
33 0.1 x 0.9 =
44 0.8 x 0.3 =
11 0.4 x 0.7 =
Modeling Decimal Multiplication
0.30
0.09
0.24
pull for problem
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Guided Practice
4 x 0.5 = _____
9 x 0.2 = _____
6 x 0.23 = _____
1.8
2.0
1.38
SolutionSolution
SolutionSolution
SolutionSolution
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=
= n3 x 0.4
n = 1.20SolutionSolution
Multiply Decimals by Whole Numbersexample
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6.4x 5
6x 5 30
PullPull
0.989x 27
1x 27 27
PullPull
Estimate Decimal Products
To estimate decimal products, round each factor to the first
significant (non-zero) digit or nearest whole number.
(Pull for examples)
Estimating the product can help you correctly
position the decimal point in the product.
PullPull
Position the decimal point show a reasonable the product.
.
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The number of decimal places in the product is equal to the sum of the number of decimal places in the factors.
3.
Hit th
e bull
's ey
eMultiplying when one or more of the
factors is a decimal number is like
multiplying with whole numbers.
Multiply Decimals
9.01x 6.8 72085406061 268
Remember!You can use your estimate to check your decimal placement in the product.
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Using Decimal Multiplication
The average lab rat weighs 0.425 kilogram. If there are 15 rats in the lab, how much do they weigh altogether?
The Boston Marathon is about 26 miles. A mile is equal to 1.609 kilometers. How many kilometers does a runner who completes the race run?
work space
work space
6.375
41.834
SolutionSolution
SolutionSolution
December 10, 2015
How to Multiply Decimals:
Multiply decimals just as if they were whole numbers.
3.772.8
3016754
10.556
x _____
_____+
Click beside 3.77 to place the decimal point.
(2 decimal places)
(1 decimal place)
(3 decimal places)10 556
Click me to check the product.
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x =
x x =
0.073 x 0.375
x =
9.56 x 0.345
0.019 x 0.67 x 0.97
Use rounding to estimate products
10 x 0.3 = 3
0.07 x 0.4 = 0.028
0.02 x 0.7 x 1 = 0.014
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0.013 x 0.232
97.04 x 27.25
0.352 x 27.1
Use rounding to choose the most reasonable answer
9.5392 95.3920.95392
2,644.34 26,443.4264.434 264,434
953.92
0.3 x 30
100 x 30
0.0003016 0.03016 0.30160.003016
0.01 x 0.2 = 0.0020.003016
2,644.34
9.5392
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Practice Multiplying
.076x___
.056
.0076x___
.6x 7___
.9
.06x___.8.07x___
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Content/writing space
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Content/writing space
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Content/writing space
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Content/writing space
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Homework
p 58 # 9 - 12, 17, - 20
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Dividing Decimals
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Dividing with powers of ten
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1. Dividing a Decimal Number by a Whole Number
To divide a decimal number by a whole number:
• Use Long Division (ignoring the decimal point)
• Then put the decimal point in the same spot as the dividend (the number being divided)
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Example: Divide 9.1 by 7
Ignore the decimal point and use Long Division:
137 )91 9 7 21 21 0
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Practice
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Put the decimal point in the answer directly
above the decimal point in the dividend:
1.37 )9.1The answer is 1.3
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2. Dividing by a Decimal NumberBut what if you want to divide by a Decimal Number?The trick is to convert the number you are dividing by to a whole number first, by shifting the decimal point of both numbers to the right:
Now you are dividing by a whole number, and can continue as normal.It is safe to do this if you remember to shift the decimal point of both numbers the same number of places.
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Example 2: Divide 5.39 by 1.1You are not dividing by a whole number, so you need to move the decimal point so that you are dividing by a whole number:
move 1 1.1115.39
53.9move 1
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Since you have to move the decimal 1 time to the right so that 1.1 no longer has a decimal, you must also move the decimal in 5.39 once to the right. You are now dividing by a whole number, so you can proceed:Ignore the decimal point and use Long Division: 04911 )539 5 0 53 44 99 99 0
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Put the decimal point in the answer directly above the decimal point in the dividend:
04.911 )53.9The answer is 4.9
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How to Divide Decimals:
16.9 6.5 6.5 16.9
Study this example:
Move the decimal in the divisor to the right to make a whole number. Move the decimal the same number of places in thedividend. Then divide as usual.
PullPull
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Practice Dividing
5.7 0.3 19
3.2 0.2 16
9.6 0.4 24
1.86 0.03 62
1.74 0.03 58
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÷ =
0.874 ÷ 0.295
÷ =
÷ =x
0.442 ÷ 1.87
0.095 x 3.21 ÷ 9.56
Use rounding to estimate quotients
0.9 ÷ 0.3 = 3
0.4 ÷ 2 = 0.2
0.1 x 3 ÷ 10 = 0.03
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December 10, 2015
Answer the following2
6 - 1 × 0 + 2 ÷ 2
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Now try this one3
6 ÷ 2(1 + 2)
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Order of Operations
B - bracketsE- exponentsD - divideM - multiplyA - additionS - subtraction
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4 + 5 x 6 = 34
(5 + 5)2 = 100
102 + (3 x 8) - 14 x 2 = 96
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3 x (4 + 7) = 33
6 + 9 x 5 = 51
115 - 102 + 3 x 5 = 30
(8 + 42) ÷ 5 = 10
1 + 2 x 32 = 19
MAGIC TUNNEL
Solve the equations.Drag through the tunnelto reveal the solution.
December 10, 2015
14 - 7 + 5 + 1 = 13
15 + 10 x 4 = 55
10 - 4 ÷ 2 x 3 = 4
9.5 x 2 ÷ 0.5 + 45 ÷ 5 = 47
(18 - 11) x 3 + 7 = 28
Solve the equations.Drag through the tunnelto reveal the solution.
MAGIC TUNNEL
December 10, 2015