Primary 4 Mathematics Decimals My Pals Are Here, Book B, Chapter 10: Decimals Shaping Maths, Book B, Unit 1: Decimals

All about Decimals What do you know about Decimals? Where do you find decimals? Why do we learn about decimals? How does Decimal help us in our daily life?

Chapter Learning Outcomes Express tenths as decimals Express hundredths as decimals Express thousandths as decimals Compare and order decimals Complete number patterns Round decimals Convert a fraction to a decimal Convert a decimal to a fraction

Express Tenths as Decimals The rectangle is divided into 10 equal parts. Each part represents one tenth. We write one tenth as or 0.1. We read 0.1 as zero point one. 0.1 is a decimal.

Tenths can be represented on a number line. Express Tenths as Decimals Tenths can be represented on a number line. 1 one = 10 tenths

Express Tenths as Decimals Express 27 tenths as a decimal. 27 tenths We read 2.7 as two point seven. 2 ones 7 tenths = = 2.7

Express Tenths as Decimals 2.7 can be represented as shown. 2 ones 7 tenths = 2.7 2.7 has one decimal place. Ones 2 7 Tenths stands for 2 ones stands for 7 tenths

Express Tenths as Decimals 2.7 = 2 + 0.7 The value of the digit 7 is 0.7. The digit 7 is in the tenths place. The value of the digit 2 is 2. The digit 2 is in the ones place.

Express Tenths as Decimals We can read measurements to one decimal place. Length of chalk = 3.4 cm Length of string = 4.8 cm

Complete the table below. Fraction Decimal Let’s Try! Complete the table below. Fraction Decimal 4.3 0.7 kg 42.9 kg m 0.3 m

a) In 21.3, the digit ____ is in the tenths place. Let’s Try! Fill in the blanks. a) In 21.3, the digit ____ is in the tenths place. b) In 16.7, the value of the digit 7 is ____. c) _____ = 5 + 0.6 d) _____ + 2 + 0.5 = 52.5 3 0.7 5.6 50

Let’s Try! Express as a decimal. Express 1 as a decimal. Express 0.6 as a fraction in its simplest form. Express 1.2 as a fraction in its simplest form. Express as a decimal in its simplest form. Express 7 tenths as a decimal. Express 23 tenths as a decimal. In 28.3, the value of the digit 3 is _______. _____ + 0.2 + 0.5 = 1

Express Hundredths as Decimals The square is divided into 100 equal parts. Each part represents one hundredth. We write one hundredth as or 0.01. We read 0.01 as zero point zero one. 0.01 is a decimal.

Express Hundredths as Decimals Hundredths can be represented on a number line. 1 tenth = 10 hundredths

Express Hundredths as Decimals Express 337 hundredths as a decimal. We read 3.37 as three point three seven. 337 hundredths 3 ones 37 hundredths = = 3.37

3.37 can be represented as shown. Express Hundredths as Decimals 3.37 can be represented as shown. 3 ones 3 tenths 7 hundredths = 3.37 3.37 has two decimal places. 7 Ones 3 Tenths Hundredths stands for 3 ones stands for 3 tenths stands for 7 hundredths

Express Hundredths as Decimals 3.37 = 3 + 0.3 + 0.07 The value of the digit 7 is 0.07. The digit 7 is in the hundredths place. The value of the digit 3 is 0.3. The digit 3 is in the tenths place. The value of the digit 3 is 3. The digit 3 is in the ones place.

Complete the table below. Fraction Decimal Let’s Try! Complete the table below. Fraction Decimal 55.65 15.07 litres 0.03 litres m 2.04 m

a) In 24.57, the digit ____ is in the hundredths place. Let’s Try! Fill in the blanks. a) In 24.57, the digit ____ is in the hundredths place. b) In 5.92, the value of the digit 2 is _____. c) _____ = 4 + 0.6 + 0.03 d) 10 + 9 + 0.1 + _____= 19.19 7 0.02 4.63 0.09

Let’s Try! Express 10 tenths as a decimal. Express 90 tenths as a decimal. Express 100 hundredths as a decimal. d) Express as a decimal. e) Express 0.35 as a fraction in its simplest form. f) Express 1.28 as a mixed number in its simplest form.

We can write money as decimals. Express Hundredths as Decimals We can write money as decimals. $1.00 = ten 10¢ = 100¢ 5¢ = $0.05 10¢ = $0.10 $ 1 8 . 5 5 $ 0.50 $ 0.05 $ 10.00 $ 8.00

Express each amount in dollars. a) 65¢ = _____________ Let’s Try! Express each amount in dollars. a) 65¢ = _____________ b) 80¢ = _____________ $0.65 $0.80 Express each amount in decimal form. a) 12 dollars 45 cents = _____________ b) 25 dollars 5 cents = _____________ $12.45 $25.05

Express Thousandths as Decimals of the square is shaded. Each square is divided into 10 equal parts. Each part represents one thousandth.

Express Thousandths as Decimals We write one thousandth as or 0.001. We read 0.001 as zero point zero zero one. We write five thousandths as or 0.005. We read 0.005 as zero point zero zero five.

1 hundredth = 10 thousandths Express Thousandths as Decimals Thousandths can be represented on a number line. 1 hundredth = 10 thousandths

Express as a decimal. Express Thousandths as Decimals = 2.534 = 5 tenths 3 hundredths 4 thousandths = 2.534

Express Thousandths as Decimals 2.534 can be represented as shown. 2 ones 5 tenths 3 hundredths 4 thousandths = 2.534 2.534 has three decimal places. 3 Ones 2 5 Tenths Hundredths Thousandths 4 stands for 2 ones stands for 5 tenths stands for 3 hundredths stands for 4 thousandths

Express Thousandths as Decimals 2.534 = 2 + 0.5 + 0.03 + 0.004 The value of the digit 4 is 0.004. The digit 4 is in the thousandths place. The value of the digit 3 is 0.03. The digit 3 is in the hundredths place. The value of the digit 5 is 0.5. The digit 5 is in the tenths place. The value of the digit 2 is 2. The digit 2 is in the ones place.

Complete the table below. Fraction Decimal Let’s Try! Complete the table below. Fraction Decimal 0.603 2.034 km 81.246 km

a) In 3.987, the digit ____ is in the thousandths place. Let’s Try! Fill in the blanks. a) In 3.987, the digit ____ is in the thousandths place. b) In 8.023, the value of the digit 3 is _____. c) 1.036 = 1 + _____ + 0.006 d) 6 + 0.4 + 0.05 + 0.006 = _____ 7 0.003 0.03 6.456

3 ones is greater than 2 ones. So, 3.4 is greater than 2.9. Compare and Order Decimals Which is greater, 3.4 or 2.9? Ones 3 4 Tenths Thousandths Compare the ones. 2 9 3 ones is greater than 2 ones. So, 3.4 is greater than 2.9.

Which is greater, 2.036 or 2.306? Compare and Order Decimals Ones 2 Tenths Hundredths Thousandths 6 Compare the ones. They are the same. 2 3 6

3 tenths is greater than 0 tenths. So, 2.306 is greater than 2.036. Compare and Order Decimals Which is greater, 2.036 or 2.306? 3 Ones 2 Tenths Hundredths Thousandths 6 Compare the tenths. 2 3 6 3 tenths is greater than 0 tenths. So, 2.306 is greater than 2.036.

Arrange 0.011, 0.101 and 0.01 in decreasing order. Compare and Order Decimals Arrange 0.011, 0.101 and 0.01 in decreasing order. Compare the ones. They are the same. 1 Ones Tenths Hundredths Thousandths 1 1 1

Arrange 0.011, 0.101 and 0.01 in decreasing order. Compare and Order Decimals Arrange 0.011, 0.101 and 0.01 in decreasing order. 1 Ones Tenths Hundredths Thousandths Compare the tenths. 1 1 1 1 tenth is greater than 0 tenths. So, 0.101 is the greatest.

Arrange 0.011, 0.101 and 0.01 in decreasing order. Compare and Order Decimals Arrange 0.011, 0.101 and 0.01 in decreasing order. Compare the hundredths of the remaining numbers 0.011 and 0.01. They are the same. 1 Ones Tenths Hundredths Thousandths 1 1 1

Arrange 0.011, 0.101 and 0.01 in decreasing order. Compare and Order Decimals Arrange 0.011, 0.101 and 0.01 in decreasing order. 1 Ones Tenths Hundredths Thousandths Compare the thousandths. 1 1 1 0 thousandths is smaller than 1 thousandth. So, 0.01 is the smallest. In decreasing order, the decimals are 0.101, 0.011 and 0.01.

a) Arrange these decimals in decreasing order. Let’s Try! a) Arrange these decimals in decreasing order. 21.03, 20.031, 21.301 _______ , _______ , _______ 21.301 21.03 20.031 b) Arrange these decimals in increasing order. 5.208, 5.828, 5.802 _______ , _______ , _______ 5.208 5.802 5.828

What is 0.1 more than 3.1? 0.1 more than 3.1 is 3.2. Complete Number Patterns What is 0.1 more than 3.1? 0.1 more than 3.1 is 3.2.

Look at the number pattern below. What are the next two decimals? Complete Number Patterns Look at the number pattern below. What are the next two decimals? + 0.1 + 0.1 + 0.1 + 0.1 1.3, 1.4, 1.5, ______, ______ 1.6 1.7

What is 0.01 less than 2.34? 0.01 less than 2.34 is 2.33. Complete Number Patterns What is 0.01 less than 2.34? 0.01 less than 2.34 is 2.33.

Look at the number pattern below. What are the next two decimals? Complete Number Patterns Look at the number pattern below. What are the next two decimals? − 0.01 − 0.01 − 0.01 − 0.01 3.065, 3.055, 3.045, ______, ______ 3.035 3.025

What is 0.001 more than 0.335? 0.001 more than 0.335 is 0.336. Complete Number Patterns What is 0.001 more than 0.335? 0.001 more than 0.335 is 0.336.

Look at the number pattern below. What are the next two decimals? Complete Number Patterns Look at the number pattern below. What are the next two decimals? + 0.001 + 0.001 + 0.001 + 0.001 8.2, 8.201, 8.202, ______, ______ 8.203 8.204

Fill in the blanks. ______ is 0.1 less than 20.45. Let’s Try! Fill in the blanks. ______ is 0.1 less than 20.45. ______ is 0.01 more than 6.728. 9.305 is 0.001 less than ______. 20.35 6.738 9.306

Complete the number patterns. Let’s Try! Complete the number patterns. 17.12, 17.22, ______, 17.42, 17.52, 17.62 1.605, 1.585, 1.565, ______, 1.525, 1.505 1.20, 1.205, 1.21, 1.215, 1.22, ______ 17.32 1.545 1.225

Round Decimals A piece of wire is 2.2 m long. Let’s look at the decimal 2.2 on the number line. 2.2 2 3 2.5 2.2 is between 2 and 3. 2.2 is nearer to 2 than to 3. 2.2 m is 2 m when rounded to the nearest metre. 2.2 m ≈ 2 m

Round Decimals A melon has a mass of 1.26 kg. Let’s look at the decimal 1.26 on the number line. 1.26 1.2 1.3 1.25 1.26 is between 1.2 and 1.3. 1.26 is nearer to 1.3 than to 1.2. 1.26 kg is 1.3 kg when rounded to 1 decimal place. 1.26 kg ≈ 1.3 kg

Round Decimals Round 2.735 to 2 decimal places. Let’s look at the decimal 2.735 on the number line. 2.735 2.73 2.74 2.735 2.735 is exactly halfway between 2.73 and 2.74. 2.735 is 2.74 when rounded to 2 decimal places. 2.735 ≈ 2.74.

Round Decimals When the digit in the tenths place is smaller than 5, 6 7 6.1 6.2 6.3 6.4 When the digit in the tenths place is smaller than 5, the number is rounded down to the smaller whole number. 6 7 6.5 6.6 6.7 6.8 6.9 When the digit in the tenths place is 5 or greater than 5, the number is rounded up to the greater whole number.

Round Decimals 6.1 6.2 6.11 6.12 6.13 6.14 When the digit in the hundredths place is smaller than 5, the number is rounded down to the smaller tenth. 6.1 6.2 6.15 6.16 6.17 6.18 6.19 When the digit in the hundredths place is 5 or greater than 5, the number is rounded up to the greater tenth.

Round Decimals 6.11 6.12 6.111 6.112 6.113 6.114 When the digit in the thousandths place is smaller than 5, the number is rounded down to the smaller hundredth. 6.11 6.12 6.115 6.116 6.117 6.118 6.119 When the digit in the thousandths place is 5 or greater than 5, the number is rounded up to the greater hundredth.

the nearest whole number Let’s Try! Complete the table below. Decimal Rounded to: the nearest whole number 1 decimal place 2 decimal places 1.404 3.289 kg 2.327 km 8.917 cm 9.995 litres 2.553 g 7.068 1 1.4 1.40 3 kg 3.3 kg 3.29 kg 2 km 2.3 km 2.33 km 9 cm 8.9 cm 8.92 cm 10 litres 10.0 litres 10.00 litres 3 g 2.6 g 2.55 g 7 7.1 7.07

Convert a Fraction to a Decimal I know that and How can I convert fractions that do not have denominator 10 or 100 to decimals?

Convert a Fraction to a Decimal Express each of the following as a decimal. a) Find the equivalent fraction with a denominator of 10 or 100 first. = 0.5 b) = 0.06 c) = 2.04

Express each fraction as a decimal. Let’s Try! Express each fraction as a decimal. a) b) c) d) 0.12 0.25 7.4 3.46

Convert a Decimal to a Fraction Express each of the following as a fraction or a mixed number in its simplest form. Write the decimal as a fraction with a denominator of 10 or 100 first and then express it in its simplest form. a) 0.6 b) 0.28 c) 3.15

Let’s Try! Express each decimal as a fraction or a mixed number in its simplest form. a) 0.75 b) 3.05 c) 5.25 d) 1.82

Express tenths as decimals Reference — Textbooks Learning Outcomes Express tenths as decimals 4B pp. 53 – 57 pp. 4 – 12 Express hundredths as decimals pp. 58 – 63 pp. 13 – 20 Express thousandths as decimals pp. 64 – 67 pp. 21 – 24 Compare and order decimals pp. 68 – 76 pp. 12, 17, 19, 20, 24

Complete number patterns Reference — Textbooks Learning Outcomes Complete number patterns 4B pp. 73 – 74 4B pp. 23 Round decimals pp. 77 – 81 pp. 25 – 30 Convert a fraction to a decimal pp. 82 – 83 pp. 8, 16, 22 Convert a decimal to a fraction pp. 84 – 85