Name: Homeroom:

Decimals

Student Learning Expectations

Outcome

I can develop number sense by:

Checking for

Understanding

demonstrating an understanding of place value, including numbers that are less than one

thousandths.

solving problems involving decimals.

demonstrating an understanding of multiplication and division of decimals (1-digit whole

number multiplies and 1-digit natural number divisors).

2

Representing Decimals

1. Write the decimal to represent each shaded area using both numerals and words.

a)

b)

c)

2. Write each decimal in words.

a) 81.9 =

b) 40.12 =

c) 28.592 =

d) 30.700 =

3. Write each word as a number.

a) two hundred ninety and eight tenths =

b) one thousand forty-two and sixteen hundredths =

c) sixty-seven and ten thousandths =

d) seven hundred two and forty-six thousandths =

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4. Write the place value of the underlined digit.

a) 4 793.6 =

b) 36.4 =

c) 387.5 = d) 2 078.123 =

e) 412.939 = f) 32.76 =

5. Write < or > or = between each pair of numbers.

a) 38.4 34.7 b) 56.9 65.9 c) 42.5 42.0

d) 184.03 184.30 e) 397.765 397.80 f) 69.40 69.35

g) 145.709 145.80 h) 401.10 401.01 i) 6.900 6.90

4

I can demonstrate understanding of place value

for numbers less than one thousandth.

1. Create a place-value chart below and show each number in it.

a) 3.4715 b) 0.003 025 c) 1.250 43 d) 0.0053

a)

b)

c)

d)

2. Use the numbers in question 1. What is the value of the 3 in each number?

a) b) c) d)

3. Write each number in standard form.

a) 3 and 124 thousandths

b) 15 and 6 thousandths

c) 7 ten-thousandths

d) 13 millionths

e) 4 and 21 hundred-thousandths

f) 368 ten thousandths

4. Write a number that has a 4 in:

a) the tenths position b) the millionths position

c) the thousandths position d) the hundred-thousandths position

e) the ten-thousandths position f) the ones position

5

_________

5. Write each number in expanded form.

a) 2.000 081

b) 0.0435

c) 0.000 935

d) 0.012 78

6. Write the number in each fact in as many different forms as you can.

a) The diameter of a strand of sewing thread is about 0.030 48 cm.

b) The mass of a fine grain of sand is about 0.000 67 g.

7. How are the values of the 5s in each number related? How many times bigger or smaller is

one five from the other five? a) 5.005

b) 0.355

c) 0.500 53

d) 2.351 529

6

Adding and Subtracting Decimals

1. Estimate each sum.

a) 132.254 + 21.2 d) 2.26 + 0.064 + 6

b) 36.2 + 2.16 e) 8 + 0.23 + 7.663

c) 2.94 + 0.028 f) 0.99 + 32.8 + 76.021

2. Estimate each difference.

a) 6.75 - 4.25 d) 4.88 – 1.99

b) 8.20 - 4.15 e) 7.45 – 6.95

c) 9.00 - 8.35 f) 8 – 1.99

3. Complete the chart.

Number Sentence Estimated Answer Actual Answer

a) 5.44 + 6.3 + 2.012

b) 6.01 – 4.999

c) 4.311 + 5 + 7.3

d) 7.99 – 5.854

e) 3.21 + 12.3 + 6

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4. Use the problem solving process to solve:

a) Gabrielle has $20.00. She is purchasing items for lunch. She bought a sandwich for $3.99, a

pop for $1.29 and chips for $1.55. How much change will Gabrielle get back?

b) Matthew is tying ribbon together to outline a picture frame. He tied 4.5cm, 1.002cm, 5.643cm

and 12.3cm. If the perimeter of the picture frame is 25 cm, does Matthew have enough ribbon to

go around the frame?

8

I can solve problems involving decimal numbers.

1. Estimate then calculate each sum or difference.

a) 6.23 + 5.004 b) 4.8 – 1.27

c) 10.678 - 9.02 d) 21.73 + 4.907

e) 29.311 – 13.8 f) 97.113 + 24.52

2. Shawn and his brothers went to the movie theatre. One ticket cost $7.75.

a) Estimate the cost of 3 tickets.

b) Shawn paid $10.75, including tax, for 3 containers of popcorn. Estimate the cost of one

container of popcorn.

3. It costs $17.85 per night to camp at Notikewin Provincial Park in Alberta. About how much

will it cost to camp there for a week?

4. Demonstrate how you know if the sum or difference is greater than or less than the target

number. a) Is 7.26 + 21.088 greater than, or less than, 28?

b) Is 41.16 – 40.027 greater than, or less than, 1?

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Multiplying Decimals

1. How many decimals places are in each of the following?

a) 8.6 x 6 c) 15.11 x 2

b) 9.17 x 2 d) 355.551 x 7

2. Calculate.

a) 7.12 x 4 d) 8.7 x 3

b) 20.14 x 3 e) 356.1 x 4

c) 8.09 x 9 f) 80.112 x 7

3. Predict the order of products from least to greatest. Check your prediction by calculating.

Predicted order:

a) 3.25 x 6 c) 7.1 x 5

b) 10.31 x 2 d) 11.901 x 9

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4. Solve the word problem

a) Julie is buying apples at the grocery store. Apples cost $0.75/kg. If Julie bought 6 kg of

apples, how much does it cost Julie for the apples?

b) Dora’s garden is 1.3 m by 6 m in area. Joseph’s garden is 0.91 m by 9 m in area. Who’s

garden has the greatest area?

c) Yan is build a rectangular dog kennel. The dog kennel measures 2.95 m by 5 m. Yan wants to

lay out rocks in the dog kennel. If the rocks cost Yan $12.99 per square m, how much will is cost

her to cover the kennel floor?

d) Louise is treating herself and 5 friends to the movies. If she bought everyone tickets, pop and

popcorn, how much change will she have remaining is she brought $50.00?

Admission - $8.50

Pop - $3.25

Popcorn - $4.75

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I can demonstrate understanding of

multiplication of decimals.

1. Multiply.

a) 0.43 x 5 b) 0.065 x 2 c) 0.24 x 3

2. Multiply. Record each product in the place-value chart.

Ones Tenths Hundredths Thousandths Ten-Thousandths

a) 0.008 x 7 b) 0.041 x 4 c) 0.0209 x 5

d) 0.184 x 6 e) 0.1258 x 9 f) 0.0491 x 3

3. Multiply. What patterns do you see?

a) 0.8 x 4 b) 0.39 x 8 c) 0.027 x 6

0.08 x 4 0.039 x 8 0.0027 x 6

0.008 x 4 0.0039 x 8 0.000 27 x 6

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4. Leah cut a strip of leather into 7 equal lengths to make bookmarks.

Each piece was 0.232 m long. a) How long was the strip of leather before Leah cut it?

b) How many cuts did she make?

5. Multiply as you would whole numbers. Estimate to place the decimal point.

a) 0.495 x 6 b) 0.0027 x 9 c) 0.093 x 3

d) 0.74 x 7 e) 0.0053 x 8 f) 0.089 x 5

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7 56.7

8 71.6

8 9.28

Division of Decimal Numbers

1. Divide each of the following:

a) 8 7.20 b) c)

2. Find the quotient for each of the following:

a) 7 54.6 b) c)

d) 4 76.4 e) f)

3. Flip each division sentence to vertical and solve.

a) 74.4 8 = b) 3.12 6 = c) 8.1 9 =

9 90.9

6 57.6

5 83.5

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4. Solve the word problem

a) Jaela has $32.45 in her bank. She wants to buy Christmas presents for 5 people. How much

can she spend evenly on each person?

b) Mrs. Tyslau went to the store. Chips were either 2 for $3.46 or 3 for $4.14. Which is the

better deal?

15

I can demonstrate understanding of

division of decimals.

1. Estimate to choose the correct quotient for each division question.

2. Divide. Estimate to place the decimal point.

a) 3.589 ÷ 2 b) 18.2 ÷ 4 c) 2.768 ÷ 5

d) 14.07 ÷ 5 e) 49.77 ÷ 2 f) 4.592 ÷ 4

3. Divide. Write each quotient to the same number of decimal places as there are in the

dividend. a) 3.189 ÷ 2 b) 5.1 ÷ 9 c) $2.05 ÷ 2

d) 27.3 ÷ 4 e) 7.66 ÷ 3 f) 1.3 ÷ 6

4. Lisa divided a 1.89-L bottle of cranberry juice equally among 6 glasses. How much juice is in

each glass?

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5. Three friends take a taxi home from the baseball game. The taxi ride was $35.80.

They want to share the cost equally. a) How much should each person pay?

b) Is your answer to part an exact or approximate? Explain.

c) Is it possible to share the cost equally? Explain.

6. Check each division below. For each incorrect quotient, explain the error, then write the

correct quotient. a) 1.76 ÷ 4 = 0.44

b) $10.88 ÷ 5 = $2.176

c) 18.46 L ÷ 3 = 6.153 L

d) 9.544 ÷ 4 = 23.86

7. Write the place value to make each statement true.

a) 12 hundredths ÷ 4 = 3

b) 42 thousandths ÷ 6 = 7

c) 49 millionths ÷ 7 = 7

d) 264 ten-thousandths ÷ 2 = 132

8. Find each quotient. What patterns do you see?

a) 0.4 ÷ 2 = b) 0.32 ÷ 8 = c) 0.075 ÷ 5 =

0.04 ÷ 2 = 0.032 ÷ 8 = 0.0075 ÷ 5 =

0.004 ÷ 2 = 0.0032 ÷ 8 = 0.000 75 ÷ 5 =

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Show What You Know Review

1. Write each number is Standard Form. (4 marks)

a) 2 and 12 ten-thousandths __________________________

b) 7 millionths __________________________

c) 16 and 46 hundred-thousandths __________________________

d) 1 and 51 millionths __________________________

2. How are the values of the underlined digits in each number related?(4 marks)

a) 0.626 __________________________________________________

b) 5.489 48 ___________________________________________________

c) 0.000 355 ___________________________________________________

d) 9.39 ___________________________________________________

3. The Bigleaf Maple tree is native to the Queen Charlotte Islands. It produces winged seeds

that can be carried long distances by the wind. A seed has a mass of about 0.126 582g.

Write this number as many ways as you can.

(6 marks)

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4. Estimate and then tell if your estimate is an overestimate or an underestimate. (6 marks)

a) 6.23 x 4 _______________________ d) 21.872 x 3 ___________________

b) 9.49 x 7 _______________________ e) 18.39 ÷ 3 ____________________

c) 125.431 ÷ 5 ____________________ f) 19.8 ÷ 4 _____________________

5. The decimal point is missing in each product. Rewrite the product and place the decimal

point in the correct spot. (6 marks)

a) 6.9 x 7 = 483 b) 7.53 x 3 = 2259 c) 11.288 x 4 = 45152

d) 2.307 x 5 = 11535 e) 3.005 x 4 = 1202 f) 4.916 x 5 = 2458

6. The Giant Fan Palm produces the world’s largest seed. A seed has a mass of about 9.075

kg. What is the combined mass of 6 of these seeds? (3 marks)

7. Multiply (6 marks)

a) 0.321 x 6 b) 0.0249 x 5 c) 0.0043 x7

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8. The recipe Sebastian wants to make requires 1.5 L of evaporated milk. He has four 0.385

L cans. Does he have enough milk? (3 marks)

9. Estimate each quotient. (6 marks)

a) 36.57 ÷ 6 ________ b) 22.41 ÷ 4 _________ c) 4.189 ÷ 2 _________

d) 42.3 ÷ 9 _________ e) 8.27 ÷ 4 __________ f) 7.1348 ÷ 8 _________

10. Estimate to choose the correct quotient for each division question. (3 marks)

Question Possible Quotients

a) 9.348 ÷ 3 3.116 31.16 311.6

b) 52.925 ÷ 5 0.105 85 1.0585 10.585

c) 1.888 ÷ 8 0.236 2.36 23.6

11. James Steacy of Saskatoon won the silver medal in the men’s discus throw at the 2006

Commonwealth Games in Melbourne, Australia. In the finals, James threw the discus 6

times for a total distance of 431.94 m. About how far did he throw each discus? (3 marks)

12. Divide. (12 marks)

a) 24.15 ÷ 6 b) 31.87 ÷ 8 c) 9.3 ÷ 6

e) 14.523 ÷ 4 e) 3.5 ÷ 9 f) 11.68 ÷ 9

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13. The Coulter Pine produces the world’s most massive pine cones. The combined mass of 8

of these cones is 25.259 kg. Find the mass of one Coulter Pine cone to the nearest

hundredth of a kilogram. (3 marks)

14. Divide. (12 marks)

a) 0.58 ÷ 8 b) 0.066 ÷ 4 c) 0.142 ÷ 8

f) 0.0075 ÷ 6 e) 0.081 ÷ 6 f) 0.09 ÷ 5

15. Darcy takes one chewable multivitamin each morning. Each week, Darcy gets 0.0119 g of

riboflavin from the vitamins. How much riboflavin is in one multivitamin? Show your

work. (3 marks)