Unit Two - Operations with decimals
Unit Two - Operations with Decimals Introduction (or re-introduction) to place value Read the following numbers (properly!) 145 2.35 1 567 043.793 Place Value
1,000,000 100,000 Place Value millions hundred thousands ten-thousands 10,000 thousands 1000 100 10 1 0.1 hundreds tens ones tenths hundredths 0.01 0.001 thousandths ten-thousandths 0.0001
Place Value Teacher's Notes 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 tenths hundredths thousandths ten thousandths 1,356,426.7142 decimal point Example ones tenths hundredths
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. 3.085 1,085.06
Write the number in expanded notation 12.25 308.4 2400.054 2 x 1000 + 4 x 100 + 5 x 0.01 + 4 x 0.001
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)
Standard Form Words To 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. 9.075 Click to hear number said in words. 0.405 3.007 13.28
Going from words to standard (number) form: Ex: Three hundred sixteen and fifteen thousandths Tells you where the decimal part ends 316.015 thirty-four and sixteen hundredths one hundred twenty-two thousandths eleven and three hundredths 11.03 34.16 0.122
Match the number in standard form and in words. 50.45 318 0.318 9.09 0.909 5.045 1 2 3 4 5 6 Click on a number to hear it said in words.
Drag the numbers to the right to reveal the number in words. 44.04 4.404 forty-four and four hundredths 0.46 forty-six hundredths four and four hundred four thousandths 4.6 four and six tenths 440.4 four hundred forty and four tenths 0.046 forty-six thousandths
Round off to Number of Digits Round off the number 56.782398 to three decimal places. Teacher's Notes 5 6. 7 8 2 3 9 8
Activity Write the correct round off values of pi (3.1415927) to the specified number of digits. Teacher's Notes 0 decimal digits 1 decimal digit 2 decimal digits 3 decimal digits 4 decimal digits 5 decimal digits 6 decimal digits 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 Select the correct answer.
Round off to Place Values Teacher's Notes 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 3
Activity Round off the number 78956.34854 to: Teacher's Notes Thousands Hundreds Tens Ones Tenths Hundredths Thousandths Correct Answer
Estimating with Decimals Why would we need to estimate?
Place the decimals on the number line 0.0167 0.015 0.0105 0.018 0.013
Which of the decimals round to 0.02? 0.0105 0.0167 0.013 0.015 0.018
Place the decimals on the number line 0.009 0.010 0.011 0.0104 0.00945 0.0107 0.0095
Which of the decimals round to 0.01? 0.0095 0.0104 0.009 0.010 0.011 0.00945 0.0107
Round to the highest place value 17.6 101.34 20?? 100 53.973 50? 0.9234? 0.9 0.0027? 0.003
Use rounding to estimate these sums 25.89 + 12.27 + 9.704 + + = 0.043 + 0.057 + 0.099 + + = 0.00095 + 0.578 + 0.063 + + =
Use rounding to estimate differences 86.89-9.532 - = 9 0.894-0.25 - = 0.078-0.021-0.0099 - - =
Homework Complete the Estimating side of the worksheet
Adding and Subtracting Decimals December 10, 2015
How to Add and Subtract Decimals: Adding Decimals 45.12 3.71 + 48.83 Subtracting Decimals 48.18 3.01 45.17
Adding Decimals + 9.08 16.99 + 10.34 27.56 45.33
What was Courtney's total score? 9.09 8.32 8.7 How much more did she score on the beam than the floor? 9.53
Homework Worksheet - adding and subtracting decimals p 48-51 Complete any 10 questions (1 a.b.c counts as one question)
Working with powers of ten Multiplying Decimals 1 000 000 100 000 10 000 1 000 100 10 1 0.1 0.01 0.001 0.0001 0.0001
Review: Multiplying Whole Numbers by 1, 10, 100, and 1,000. Click on each black dot to reveal answers to the problems in the second column. 2 x 1 = 2 36 x 1 = 36 2 x 10 = 20 2 x 100 = 200 36 x 10 = 360 36 x 100 = 3,600 2 x 1,000 = 2,000 36 x 1,000 = 36,000
Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000. Click on each problem's answer to see the pattern. 0.0007 x 1 = 0.0007 x 101 = 0.0007 x 100 1 2 = 0.0007 x 1,000 1 2 3 = 0.0007 0.007 0.07 0.7 The decimal point stays in the same place. The decimal point moves 1 place to the right. The decimal point moves 2 places to the right. The decimal point moves 3 places to the right.
Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000. Click on each black dot to reveal the answer for the problems. 0.521 x 1 = 0.521 The decimal point stays in the same place. 0.521 x 10 = 0.521 x 100 = 0.521 x 1,000 = 5.21 52.1 521 The decimal point moves right 1 place. The decimal point moves right 2 places. The decimal point moves right 3 places.
Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000. Help Deci the Frog jump the correct number of lily pads and reveal the answer! 0 0 0 0 2 x 10 Answer 0.002
Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000. Help Deci the Frog jump the correct number of lily pads and reveal the answer! 0 3 2 x 100 32 Answer
Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000. Help Deci the Frog jump the correct number of lily pads and reveal the answer! 3 0 1 6 8 x 1000 3,016.8 Answer
Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000. Click on each black dot to reveal the answer for the problems. 3.5 x 1 = 3.5 x 10 = 3.50 x 100 = 3.500x 1,000 = 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!
Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000. Draw Deci's path and then move Deci to the lily pad to check your answer. 0 7 0 1 6 x 1000 70,160 Answer
Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000. Draw Deci's path and then move Deci to the lily pad to check your answer. 0 4 x 100 40 Answer
Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000. Move the decimal point to the correct postion and then click on Deci to check your answer! 0.542 X 10 = 0 5 4 2 5.42 $6.75 x 100 = $6 7 5 $675 1000 x 0.5 = 0 5 500 You may need to add zeroes as placeholders.
Decimals Continue the pattern with decimal powers of ten.
Multiplying Decimals Use estimation to help determine if your answers are correct.
Modeling Decimal Multiplication example x = 0.8 X 0.2 = n What decimal represents the part of the whole that is orange? Click here for the 0.16 answer
Modeling Decimal Multiplication pull for problem 1 2 3 4
Guided Practice 9 x 0.2 = 1.8 Solution 4 x 0.5 = 2.0 Solution 6 x 0.23 = 1.38 Solution
Multiply Decimals by Whole Numbers example = 3 x 0.4 = n n Solution = 1.20
x 5 x 5 x 27 x 27 30 27 Estimate Decimal Products To estimate decimal products, round each factor to the first significant (non-zero) digit or nearest whole number. (Pull for examples) Pull Pull Estimating the product can help you correctly position the decimal point in the product.. Pull
Multiply Decimals. 3 the numb places in Multiplying when one or more of the factors is a decimal number is like multiplying with whole numbers. 9.01 x 6.8 7208 54060 61 268 Hit the bull's eye Remember! You can use your estimate to check your decimal placement in the product.
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? work space Solution 6.375 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 41.834 Solution
How to Multiply Decimals: 3.77 x 2.8 3016 + 754 10.556 (2 decimal places) (1 decimal place) (3 decimal places) Click beside Click me 3.77 to to check place the product. decimal point.
Use rounding to estimate products 9.56 x 0.345 x = 0.073 x 0.375 x = 0.019 x 0.67 x 0.97 x x =
Use rounding to choose the most reasonable answer 0.352 x 27.1 0.95392 9.5392 95.392 953.92 97.04 x 27.25 264.434 2,644.34 26,443.4 264,434 0.013 x 0.232 0.0003016 0.003016 0.03016 0.3016
Practice Multiplying.07.007 x 6 6 x.6 x 7.9 x.06.8 x.07
Content/writing space December 10, 2015
Content/writing space December 10, 2015
Content/writing space December 10, 2015
Content/writing space December 10, 2015
Homework p 58 # 9-12, 17, - 20
Dividing Decimals December 10, 2015
Dividing with powers of ten December 10, 2015
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)
Example: Divide 9.1 by 7 Ignore the decimal point and use Long Division: 13 7 )91 9 7 21 21 0
Practice December 10, 2015
Put the decimal point in the answer directly above the decimal point in the dividend: 1.3 7 )9.1 The answer is 1.3
2. Dividing by a Decimal Number But 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.
Example 2: Divide 5.39 by 1.1 You 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 1.1 11 5.39 53.9 move 1
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: 049 11 )539 5 0 53 44 99 99 0 December 10, 2015
Put the decimal point in the answer directly above the decimal point in the dividend: 04.9 11 )53.9 The answer is 4.9
Pull How to Divide Decimals: Study this example: 16.9 6.5 6.5 16.9
Practice Dividing 5.7 0.3 1 3.2 0.2 1 9.6 0.4 1.86 0.03 1.74 0.03
Use rounding to estimate quotients 0.874 0.295 = 0.442 1.87 = 0.095 x 3.21 9.56 x =
2 Answer the following 6-1 0 + 2 2
3 Now try this one 6 2(1 + 2)
Order of Operations B - brackets E- exponents D - divide M - multiply A - addition S - subtraction
4 + 5 x 6 = 34 (5 + 5) 2 = 100 10 2 + (3 x 8) - 14 x 2 = 96
3 x (4 + 7) = 33 6 + 9 x 5 = 51 1 + 2 x 3 2 = 19 MAGIC TUNNEL Solve the equations. Drag through the tunnel to reveal the solution. (8 + 42) 5 = 10 115-10 2 + 3 x 5 = 30
(18-11) x 3 + 7 = 28 15 + 10 x 4 = 55 MAGIC TUNNEL Solve the equations. Drag through the tunnel to reveal the solution. 10-4 2 x 3 = 4 14-7 + 5 + 1 = 13 9.5 x 2 0.5 + 45 5 = 47