🌱 Sprout · Printable packMATHEMATICS · YEAR 5

Connecting fractions and decimals

Name Date
🎯 What you'll learn - tick each one off!
📖 Learn

Tenths, hundredths and decimals

Fractions and decimals are two ways of writing the same amount. When a whole is split into 10 equal parts, each part is a tenth. As a fraction it has a denominator of 10, like 3/10. As a decimal, tenths sit in the first place after the decimal point, so 3/10 = 0.3.

When a whole is split into 100 equal parts, each part is a hundredth. As a fraction it has a denominator of 100, like 45/100. Hundredths sit in the second place after the decimal point, so 45/100 = 0.45. A single tenth is worth 10 hundredths, which is why 0.4 is the same amount as 0.40 or 40/100.

Convert 7/10 and 45/100 to decimals.

7/10 has one digit after the point, because tenths only need one place: 7/10 = 0.7.

45/100 has two digits after the point, because hundredths need two places: 45/100 = 0.45.

Check: 0.45 is also 4 tenths plus 5 hundredths, since 0.40 + 0.05 = 0.45.

Adding a zero after the last decimal digit never changes its value, so 0.6 and 0.60 are the same amount.
tenthshundredthsdecimal pointequivalent
✏️ Activity 1

Shade and convert

Shade each bar or grid below to match the fraction or decimal given, then write the missing number. Complete the table using what you have learnt.

Shade the first bar below to show 3/10, then write it as a decimal:

Shade the second bar below to show 0.6, then write it as a fraction: /10

Shade the first grid below to show 45/100, then write it as a decimal:

Shade the second grid below to show 0.07, then write it as a fraction: /100

Complete the table below.

FractionDecimal
7/10
0.9
68/100
0.03
2/10
✏️ Activity 2

Decimals on a number line

Mark a dot on the number line below for each decimal: 0.2, 0.7 and 0.45. Then answer the questions.

00.10.20.30.40.50.60.70.80.91

Which of the three decimals is closest to 1?

Which of the three decimals is smallest?

Write 0.45 as a fraction with a denominator of 100: /100

📖 Learn

Comparing decimals by place value

To compare two decimals, first compare the whole-number part on the left of the decimal point: the number with the larger whole-number part is greater. If the whole-number parts are equal, line up the place-value columns so tenths sit under tenths and hundredths sit under hundredths. If one decimal has fewer digits, write a zero at the end so both numbers have the same number of places, this does not change the value. Then compare column by column from left to right. The first column where the digits differ tells you which decimal is larger.

Compare 0.6 and 0.45.

Write both with two decimal places: 0.60 and 0.45.

The whole-number parts are equal (both 0), so compare the tenths column: 6 tenths is more than 4 tenths.

The tenths column already gives the answer: 0.60 > 0.45.

Never compare decimals by counting digits. 0.7 has fewer digits than 0.45, but 0.7 is still the larger number because tenths are worth more than hundredths.
place valuetenths columngreater thanless than
✏️ Activity 3

Greater than or less than

Compare each pair of decimals. Write < or > in the blank to make each statement true. Use place-value columns to help you decide.

  1. 0.6 0.45
  2. 0.08 0.8
  3. 0.5 0.52
  4. 0.99 1.0
  5. 0.34 0.43
  6. 0.7 0.070
✏️ Activity 4

Order fractions and decimals

Write each set of numbers in order from smallest to largest, converting any fractions to decimals first if it helps. Then answer the questions below.

Order these numbers: 0.6, 3/10, 0.45, 7/10

Order these numbers: 1/2, 0.15, 3/4, 0.6

Which of these numbers is the smallest?

  1. 0.5
  2. 3/10
  3. 0.45
  4. 0.6
  1. 0.45 is greater than 4/10.
  2. 7/10 is less than 0.6.
✏️ Activity 5

Money and measurement challenges

Solve each problem. Show your working in the space provided.

Ari saved $0.75. Bella saved 7/10 of a dollar. Who saved more, and how much more?

A jug holds 0.75 L of juice. A bottle holds 70/100 L. Which container holds more, and by how much?

Which amount of money equals 45/100 of a dollar?

  1. $4.50
  2. $0.45
  3. $45.00
  4. $0.045

Two ribbons measure 0.45 m and 7/10 m. Put them in order from shortest to longest, then find their total length in metres.

🔑 Answer sheet

For the parent or supervisor: set this page aside before handing over the worksheet.

Activity 1

  1. 0.3 (3/10 shaded on the first bar)
  2. 6/10 (0.6 shaded on the second bar; also accept 3/5)
  3. 0.45 (45/100 shaded on the first grid)
  4. 7/100 (0.07 shaded on the second grid)
  5. Table, top to bottom: 7/10 = 0.7; 0.9 = 9/10; 68/100 = 0.68; 0.03 = 3/100; 2/10 = 0.2

Activity 2

  1. Dots at 0.2, 0.7 and 0.45, as shown on the number line below.
  2. 0.7
  3. 0.2
  4. 45/100
00.10.20.30.40.50.60.70.80.91

Activity 3

  1. 0.6 > 0.45
  2. 0.08 < 0.8
  3. 0.5 < 0.52
  4. 0.99 < 1.0
  5. 0.34 < 0.43
  6. 0.7 > 0.070

Activity 4

  1. 3/10, 0.45, 0.6, 7/10 (that is, 0.3, 0.45, 0.6, 0.7)
  2. 0.15, 1/2, 0.6, 3/4 (that is, 0.15, 0.5, 0.6, 0.75)
  3. B (3/10 = 0.3, the smallest of the four)
  4. True (0.45 is greater than 4/10, since 4/10 = 0.4)
  5. False (7/10 = 0.7, which is greater than 0.6, not less)

Activity 5

  1. Bella has 7/10 = $0.70. Ari has $0.75, which is more, by $0.05.
  2. The bottle has 70/100 = 0.70 L. The jug has 0.75 L, which is more, by 0.05 L.
  3. B ($0.45)
  4. Shortest to longest: 0.45 m, then 7/10 m (0.70 m). Total length: 0.45 + 0.70 = 1.15 m.

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