Decimals Pages 60 – 95

Understanding Decimals Pages 62 – 63 Understanding Decimals Like a fraction, a decimal shows a part of a whole. Decimals divide a whole into 10 parts or 100 parts or 1,000 parts and so on. If you have used money you’ve used decimals. Decimals get their names from the number of places on the right side of the decimal point. The decimal point separates whole numbers from decimals. A place is the position for a digit. The decimal point itself does not take up a place.

_, _ _ _,_ _ _._ _ _ _ _ _ Place Value Names Pages 62 – 63 hundred thousands hundred thousandths ten thousands ten thousandths thousands hundreds hundredths thousandths millions millionths _, _ _ _,_ _ _._ _ _ _ _ _ tens ones tenths

Why do they have those names? Pages 62 – 63 Place Values Why do they have those names? 679.328 8 1000 600 70 2 100 3 10 9

Pages 62 – 63 Mixed Decimals Mixed decimals are numbers with digits on both sides of the decimal point. $4.95 is a mixed decimal. It means 4 whole dollars and 95/100 of a dollar. As you move to the right in the decimal system, each place means that the whole has been divided into more parts, therefore, the values of the decimal places get smaller.

Pages 62 – 63 Example For each number, underline the digit that is in the place named Tenths place 297.18 Thousandths place 0.04107 Circle the correct answer for the following question Which of the following tells the value of the digit 9 in the number 2.936? 9 tenths 9 hundredths 9 thousandths 9 ten-thousands

Pages 62 – 63 Group Work For each number, underline the digit that is in the place named Hundredths place 0.1389 Tenths place 0.5864 Circle the correct answer for the following question Which of the following tells the value of the digit 7 in the number 12.047? 7 tenths 7 hundredths 7 thousandths 7 ten-thousands

Page 64 Reading Decimals Remember that a decimal gets its name from the number of places at the right of the decimal point. To read a decimal, count the places at the right of the decimal point. With mixed decimals, watch for the word & which separates whole numbers from decimal fractions.

Example Page 64 Write each decimal or mixed decimal in words 0.5 = 0.5 = 0.07 = 10.402 = Five tenths Seven hundredths Ten and four hundred two thousandths

Page 65 Writing Decimals To write decimals from words, be sure that you have the correct number of decimal places. Use zeros to hold places where necessary. Remember, again, that the word & separates whole numbers from decimal fractions in mixed decimals. Watch where zeros hold places.

Example Page 65 Write the following as a decimal or a mixed decimal. Five hundred-thousandths Forty-seven thousands Forty-eight and nine tenths = 0.00005 = 0.047 =48.9

Getting Rid of Unnecessary Zero Page 66 Getting Rid of Unnecessary Zero Consider the number 020.060 & decide whether each zero is necessary. The zero left of the digit 2 is unnecessary The zero right of the 2 is necessary because it keeps the 2 in the tens place. The zero right of 6 is unnecessary The number can be correctly written as 20.06 A decimal with no whole number is often written with a zero in the units place. The decimal .8 & 0.8 are both correct forms for eight tenths.

Page 66 Example For each number, choose the correctly rewritten number. 5.0060 a) 50.6 b) 50.06 c) 5.006 d) 5.06 003.1050 a) 3.105 b) 30.105 c) 3.15 d) 30.015 0700.40 a) 70.04 b) 70.4 c) 700.04 d) 700.4 0040.0920 a) 40.92 b) 40.092 c) 4.092 d) 4.92

Changing Decimals to Fractions Page 67 Changing Decimals to Fractions To change a decimal to a fraction (or to change a mixed decimal to a mixed number), write the digits in the decimals as the numerator. Write the denominator according to the number of decimal places. Then reduce the fraction.

Page 67 Example Write each number as a common fraction or a mixed number & reduce. 0.08 3.6 0.00324 16.00004

Page 67 Group Work Write each number as a common fraction or a mixed number & reduce. 0.085 7.2 2,036.8 7.22 0.375

Changing Fractions to Decimals Page 68 Changing Fractions to Decimals Remember that a fraction can be understood as a division problem. To change a fraction to a decimal, divide the denominator into the numerator. To divide, add a decimal point & zeros to the numerator. Usually two zeros are enough. Then bring the point up in the answer.

Page 68 Example Write each fraction as a decimal. ¼ 2/9 3/5

Group Work Page 68 Write each fraction as a decimal. 2/5 6/25 1/6 3/8 5/12

Comparing Decimals Page 70 When you look at a group of decimals, it is sometimes difficult to tell which decimal is the largest. To compare decimals, give each decimal the same number of places by adding zeros. This is the same as giving each decimal a common denominator. The zeros you add do not change the value of the decimals. Don’t write the extra zeros in the final answer.

Example Page 70 In each pair, tell which decimal is larger. 0.04 or 0.008 0.328 or 0.33 0.0057 or 0.006

Page 70 Group Work Arrange each list in order from the smaller to the largest. 0.03,0.33, 0.033, 0.303 0.106, 0.16, 0.061, 0.6 0.4, 0.405, 0.45, 0.045 0.0072, 0.07, 0.027, 0.02

Pages 71 – 72 Rounding To round a number, you must know the place value of each digit in the number. To round a decimal: Underline the digit in the place to which you want to round. If the digit to the right of the underlined digit is 5 or more, add one to the underlined digit. If the digit to the right of the underlined digit is 4 or less, do not change the underlined digit. Drop the digits to the right of the underlined digit.

Pages 71 – 72 Example Round each decimal to the nearest place value given. Tenth 4.29 Hundredth 0.582 Whole number 5.4068

Pages 71 – 72 Group Work Round each decimal to the nearest place value given. Tenth 516.24 Hundredth 0.0946 Whole number 1.89

Page 73 Adding Decimals To add decimals, line up the decimal points under each other. (Remember that whole numbers have a decimal point at its right.) This makes it so that you are adding the same place values to each other. Then add

Page 73 Example Add 0.8 + 0.047 + 0.36 123 + 2.6 + 9.04 9.043 + 0.27 + 15

Group Work Page 73 Add 0.849 + 1.6 + 73 7.563 + 0.08 + 124.9 12.3 + 0.908 + 6 + 4.25 1.6 + 23 + 12.73 + 0.485

Subtracting Decimals Page 75 To subtract decimals line up the decimals with the points under each other just like in addition. Remember to put a point to the right of a whole number. Put zeros at the right until each decimal has the same number of places. You will need the zeros for borrowing.

Page 75 Example Subtract 4.2 – 3.76 0.804 – 0.1673 3.2 – 2.68

Page 75 Group Work Subtract 0.08 – 0.0156 1.4 – 0.978 0.6 – 0.059

Multiplying Decimals Pages 79 – 81 Multiply as you would any whole numbers. To find the placement of the decimal in the product (the answer) Count the decimal places in each factor (the numbers you multiplied). Put the total number of decimal places in the product. (Sometimes you will need to put extra zeros in your answer.)

Pages 79 – 81 Example Multiply 2.8 x 4.3 (0.81)(0.69) 45.21(5.6)

Pages 79 – 81 Group Work Multiply 5.6 x 0.82 (0.94)(1.8) 34.7(209)

Multiplying Decimals by 10, 100, & 1,000 Page 82 Multiplying Decimals by 10, 100, & 1,000 To multiply a decimal by 10, move the decimal point one place to the right. To multiply a decimal by 100, move the decimal point two places to the right. To multiply a decimal point by 1,000, move the decimal point three places to the right. You may have to add zeros to get enough places.

Page 82 Example Multiply 0.8 x 10 0.721 x 10 0.06 x 1,000

Page 82 Group Work Multiply $1.25 x 10 $0.60 x 100 $0.03 x 1,000

Dividing Decimals by Whole Numbers Page 86 Dividing Decimals by Whole Numbers To divide a decimal by a whole number, line up the problem carefully. Then divide as you would a whole number & bring the decimal point up into quotient (the answer) above its position in the problem. Sometimes you will need to put zeros in your answers.

Page 86 Example Divide 33.605 ÷ 65 464.31 ÷ 77 1,565.2 ÷ 43

Page 86 Group Work Divide 1.52 ÷ 19 216.6 ÷ 38 9.516 ÷ 52

Dividing Decimals by Decimals Pages 87 – 88 Dividing Decimals by Decimals To divide a decimal by a decimal, first make a new problem. Change the number you are dividing by (the divisor) into a whole number. You can change the divisor into a whole number by moving the decimal point to the right end. Then move the decimal point in the other number (the dividend) the same number of places. Sometimes you will have to put extra zeros in the dividend.

Pages 87 – 88 Example Divide 0.11648 ÷ 0.64 145.44 ÷ 3.6 0.3933 ÷ 0.19

Pages 87 – 88 Group Work Divide 0.522 ÷ 8.7 558.6 ÷ 0.06 4.48 ÷ 0.008

Dividing Whole Numbers by Decimals Page 89 Dividing Whole Numbers by Decimals To divide a whole number by a decimal, remember to put a decimal point at the right of the whole number. Then move the points in both the divisor and the dividend. You will have to put zeros in the dividend. Not every division problem comes out even. When this happens, choose a place to round to (unless it is chosen for you in the directions). Then divide one place beyond the place you want to round to.

Page 89 Example Divide 3,237 ÷ 0.039 33,040 ÷ 5.6 37,440 ÷ 0.48

Page 89 Group Work Divide 1,178 ÷ 0.019 21,546 ÷ 51.3 2,135 ÷ 4.27

Dividing Decimals by 10, 100, & 1,000 Page 90 To divide a decimal by 10, move the decimal point one place to the left To divide a decimal by 100, move the decimal point two place to the left To divide a decimal by 1,000, move the decimal point three place to the left You may have to add zeros to get enough places.

Page 90 Example Divide $20 ÷ 1,000 $540 ÷ 1,000 $650 ÷ 100

Page 90 Group Work Divide $2.19 ÷ 10 15.8 ÷ 1,000 6,954 ÷ 1,000

Dividing to Fixed Place Accuracy Page 91 Dividing to Fixed Place Accuracy Adding zeros to a division of decimals problem does not always result in a problem that divides evenly. To get a division answer that is accurate to the nearest tenth, divide to the hundredths place & round the answer to the nearest tenth. This is called dividing to fixed place accuracy.

Example Page 91 Divide. Find the answer to the nearest tenth. 6.3 ÷ 0.8 72.6 ÷ 50.3 12.3 ÷ 7

Page 91 Group Work Divide 204 ÷ 9.2 10.3 ÷ 0.35 49.5 ÷ 36