Unit 2: Decimals Decimals are a part of a whole (just like fractions) PLACE VALUE Thousands Hundreds Tens Ones Tenths Hundredths Thousandths Ten thousandths 1000 100 10 1 1 10 1 100 1 1000 1 10000 1000 100 10 1 0.1 0.01 0.001 0.0001 What is the decimal point for? To determine the position of the ones place the ones position is left of the decimal 35
Practice: What is the position of the 8 in each of the following? 380 1 855 234 0.89 8.216 245. 708 Ordering & Comparing: First look at the whole numbers Look at the tenths position the largest digit is the larger number Then look at the hundredths position, and so forth Example: Order from greatest to least: 0.36 0.058 0.375 0.4 No whole #s 0.36 0.058 0.375 0.4 3 0 3 4 10 10 10 10 6 7 100 100 Greatest to Least: 0.4 0.375 0.36 0.058 36
Practice: Place <, >, or = 23.03 23.30 101. 89 11.89 0.454 0.56 Place in order of least to greatest: 1.33 0.67 0.607 0.76 0.706 1.03 0.70,,,,,, ROUNDING: Step 1: Underline the digit to be rounded Step 2: Write the 2 possible rounding positions Step 3: Follow the rule: The digit to the right is a 4 or less, the underlined digit stays the same The digit to the right is a 5 or greater, the underlined digit becomes one greater All the remaining digits are replaced by zero Example: 69.098 round to nearest tenths 69.100 69.000 the digit to the right of 0 is a 9 = 69.100 Practice: 76.099 round to nearest tenths 0.5403 round to nearest hundredths 35.078 round to nearest ones Practice: 37
Order the following least to greatest. 25.009 2.5009 0.2509 2.509,,, Put <, >, or = 4.44 44.4 0.303 0.030 6.05 6.050 78.2 78.22 809.101 809.110 Put the following on a number line 3.7 3.45 3.92 3.05 3.67 The cashier at the restaurant is working with a calculator to get the total amount of each bill after he calculates the tax. He is confused and doesn t know what to tell the customers what they owe because there are too many numbers. Please help him decide how much each customer must pay. Customer 1: $65.5266 Customer 2: $102.7108 Customer 3: $33.8542 38
What is the position of the 6 in each number? 6502 6.502 5.62 7. 06 Circle which number is greater between the pairs. a) 4.15 and 4.16 b) 13.32 and 13.23 c) 25.05 and 24.5 d) 0.306 and 0.362 e) 103.99 and 10.399 What about time? Place in order from longest to shortest time: (distance race) 2:33 3:03 3:45 2: 29 2:59 3:19,,,,, Place in order from the slowest to fastest time: 5:003 5:030 5:303 5:330 5:033 4:599,,,,, Adding and Subtracting Decimals: 39
Line up the decimals and fill in empty space after the decimal with zeros. Example: 4.89 + 0.0074 4.8900 + 0.0074 4.8974 Example: 70 6.974 70.000-6.974 63.026 Practice: Estimate, and then find the sum. a) 3 + 212.09 + 0.1 b) 1009.2 + 14 + 222.006 + 0.76 c) 17.1 + 0.808 + 2 d) 101 + 1.01 + 10.01 + 1.101 Estimate, and then find the difference. 40
a) 205.6008 48.567 b) 707 70.7 c) 200 4.89 d) 8.4 4.066 Find the missing number. a) 43.12 + = 187.332 b) 43.1 = 6.431 c) + 17.3 = 38.1 d) 5.08 = 14.7 Answer the following questions using the decimals from the box. a) Use 2 decimals whose sum is 24.24 b) Use 2 decimals whose difference is 13.108 c) Use 3 decimals whose sum is 37.352 12.34 25.008 11.9 0.004 Multiplying Decimals 41
Multiply like whole numbers Count the digits after the decimal for each number Starting from the end of the answer, move left the number of spaces you just counted Place the decimal Example: 24.33 x 7.9 2433 x 79 3 digits after the decimal 21897 + 170310 192207 = 192.207 Practice: Find the product. 35.88 x 1.3 123.4 x 3 8.7 x 0.6 0.55 x 0.7 Scott worked 24 hours last week. He makes $9.55 per hour. He got $44.50 in tips. How much money did Scott make last week? Dividing Decimals 42
If there is no decimal outside (the divisor), divide like whole numbers, and when you get to the decimal, put it up, and then continue. 9.398 Example: 56.39 6 6 56.390-54 23-18 59-54 50 You are usually asked to go to 3 places after Practice: Find the quotient. 58.7 7 94.436 28 0.0294 6 0.63 9 48.5 10 28.16 4 43
If there is a decimal outside (the divisor), move it until the number is whole, and move the decimal inside the same number of spaces. If there are less spaces inside, add zeros. Remember, there are no remainders. 225 Example: 7.2 0.32 0.32 7.2 = 32 7200-64 80-64 160-160 0 Practice: Find the quotient. 78.5 7.23 34.416 1.8 55.3 0.9 18 2.3 Blake stacked 12 blocks which measured 45.6 centimetres. What is the height of each block? 44
Order of Operations and Decimals: follow the rules of BEDMAS Practice: 4.3 + 5 x 3.03 7.23 + 1.2 2 124.8 4.1 x (12.8 5.7) 5 3.1 2 0.4 2 + 0.55 (3.2 + 5.01) (2.3 0.58 10) 9.8 x (4.5 (1.5 0.5) 1.7 0 ) 9.8 + [4.5 1 1.5 (6.15 1.7)] 34.2 (25.3 + 0.003) 45
Decimal Practice: Find the missing number. a) 5 x = 45 b) 12 = 3.45 c) 14.3 = 5.2 d) 3.2 x = 17.92 The service elevator can lift a maximum of 650 kg. A shipment of the following just arrived. Can all the boxes be delivered in one trip on the elevator? Explain your reasoning. 52.4 kg 103.22 kg 89.3 kg 68.3 kg 131.89 kg 205.99 kg Anne stops to get gas at 97.4 cents per litre. Her total cost was $35.38. On her way home she notices the price of gas at another station was 1.6 cents cheaper. Anne is upset about the money she could have saved. How much could she have saved? 46
Extra Practice: NO CALCULATOR 33.353 + 2.08 + 8709.0035 + 11 45-9.085 231.231 x 1.2 67.9 2.3 702-70.2 47