Grade by Grade
B. Number · Number Sense: Numbers to 10 000, Fractions and Decimal Tenths

Decimal Tenths: Reading, Writing and Showing

B1.7 B1.9About 40 minutes
Learning goals
  • I can read and write decimal tenths, like 0.3 and 2.4.
  • I can explain what the decimal point does.
  • I can show decimal tenths with drawings, a metre stick and a number line.
  • I can find decimals in everyday life.

Words to know

decimal
A number that uses a decimal point to show parts of a whole, like 2.4.
decimal point
The dot that separates the whole number (on the left) from the parts of a whole (on the right).
tenth
One of 10 equal parts of a whole. 1/10 = 0.1.
tenths place
The first place to the right of the decimal point.

A new way to write tenths

In the fraction lessons, you cut wholes into 10 equal parts called tenths. There is another way to write tenths: with a decimal point.

3/10 can also be written as 0.3. Both mean three tenths.

Let's start with a story

At the school track meet, Aisha runs 100 m. The timer shows 18.4 seconds.

That means 18 whole seconds and 4 tenths of a second more. We read it as "eighteen and four tenths" seconds. Many people also say "eighteen point four".

Tenths of a second are very short. Timers use them because racers can finish very close together!

A red running track with white lane lines beside a grass field at a school.
At a track meet, race times like 18.4 seconds use tenths, because runners can finish very close together. AI-generated image
TensOnes.Tenths
18.4
0.7
3.0
Place value with tenths. The decimal point sits between the ones and the tenths. 18.4 = 1 ten, 8 ones and 4 tenths.

What the decimal point does

  • Digits to the left of the decimal point are whole numbers.
  • The first digit to the right of the decimal point is the tenths.
  • When we read a decimal, we say "and" for the decimal point: 2.4 is "two and four tenths". (That's why we don't say "and" inside whole numbers!)
  • If there are no wholes, we write a 0 before the point: 0.7, not .7. It makes the decimal point easy to see.

The times-10 pattern keeps going

Remember: each place is worth 10 times the place to its right. That pattern keeps going past the ones place:

  • 10 tenths = 1 one
  • 1 one = 10 tenths

So 1.0 and 10/10 are the same as 1 whole.

10.3
Two bars, each cut into 10 equal parts. The first is all shaded (1 whole). The second has 3 tenths shaded (0.3). Together they show 1.3.
Worked example

Example 1: Read and write decimals

Write each in words: (a) 0.6 (b) 4.9 (c) 12.1

  1. (a) 0 wholes and 6 tenths: six tenths.
  2. (b) 4 wholes and 9 tenths: four and nine tenths.
  3. (c) 12 wholes and 1 tenth: twelve and one tenth.

six tenths, four and nine tenths, twelve and one tenth

Worked example

Example 2: From words or fractions to decimals

Write as a decimal: (a) seven tenths (b) 3 and 5 tenths (c) 8/10

  1. (a) No wholes: write 0, then the point, then 7: 0.7.
  2. (b) 3 wholes, point, 5 tenths: 3.5.
  3. (c) 8 tenths: 0.8.

0.7, 3.5 and 0.8

Decimals on a number line

Split the space between 0 and 1 into 10 equal jumps. Each jump is 0.1. After 0.9 comes 1.0 (which we just call 1), then 1.1, 1.2 and so on.

00.511.52
0 to 2 with a tick every tenth. The dots show 0.3 and 1.3.

Decimals in everyday life

  • Length: A metre stick is 100 cm. Ten equal pieces of 10 cm each make 1 m, so 10 cm = 0.1 m, and a 1.5 m ribbon is 1 metre and 5 tenths of a metre.
  • Distance: a 2.5 km ski trail.
  • Temperature: 21.5 °C in the classroom.
  • Time: race times like 18.4 seconds.
  • Rain and snow: 4.6 cm of snow fell overnight.
Worked example

Example 3: Tenths of a metre

A shelf is 0.7 m long. How many centimetres is that?

  1. Each tenth of a metre is 10 cm.
  2. 7 tenths is 7 × 10 cm.

70 cm

Say tenths

Read decimals the "math" way ("four and nine tenths") at least some of the time. Saying tenths out loud reminds you what the digit after the point means.

Just for fun

Q: What did the decimal point say to the 3 and the 7 in 3.7?

A: "Stay on your own side, please! Wholes on the left, tenths on the right."

Hands-on activity

Metre stick decimals

You need: a metre stick or a tape measure, some objects at home, paper and a pencil.

  1. Look at the metre stick. Find 10 cm, 20 cm, 30 cm ... These mark the tenths of a metre: 0.1 m, 0.2 m, 0.3 m ...
  2. Measure 5 things that are less than 2 m long, like a table, a bed, a door's width, a broom, a pillow. Measure to the nearest 10 cm.
  3. Write each length in metres as a decimal. For example, a table that is about 120 cm long is 1.2 m (1 metre and 2 tenths).
  4. Write each length in words too: "one and two tenths metres".

Math talk: "Which object was closest to 1 m? Which was longer than 1.5 m?"

Your turn

1

Write 0.4 in words.

2

Write 6.8 in words.

3

Write as a decimal: nine tenths

4

Write as a decimal: 5 and 2 tenths

5

Write 3/10 as a decimal.

6

In 47.5, what is the value of the 5?

7

How many tenths make 1 whole?

More practice: warm-up

1

Write 0.1 as a fraction.

2

Write as a decimal: one and one tenth

3

Which digit is in the tenths place of 8.3?

4

What comes next? 0.6, 0.7, 0.8, ...

5

What comes after 0.9 when counting by tenths?

More practice: on your own

1

Write as a decimal: 12 and 7 tenths

2

Count by tenths from 2.7 to 3.2.

3

A ribbon is 1.4 m long. How many centimetres is that?

4

Write 2 6/10 as a decimal.

5

Max writes "three tenths" as 3.0. What is wrong? What should he write?

Challenge

1

How many tenths are in 2.5?

2

A puppy is 0.4 m tall. Its owner is 1.6 m tall. How much taller is the owner, in tenths of a metre?

3

Write a decimal with 3 digits that has 4 in the tenths place and is between 20 and 30.

Check your understanding

Quiz

1.

How do you read 5.3?

2.

Which decimal is seven tenths?

3.

Which is the same as 9/10?

4.

What is the value of the 2 in 16.2?

5.

Counting by tenths: 3.8, 3.9, ...

6.

How many centimetres are in 0.3 m?

For parents and teachers

Big idea: B1.7 asks Grade 4 students to read, represent, compare and order decimal tenths in various contexts. In Grade 4 the Ontario curriculum stops at tenths; hundredths come in a later grade. This lesson also starts B1.9 (relating fractions and decimal tenths): 3/10 = 0.3.

Common difficulties:

  • Reading 0.3 as "three" or writing three tenths as 3.0 or .3. Insist on the 0 before the point and the word "tenths".
  • Writing 3.10 after 3.9. In tenths, 10 tenths become a new whole: 3.9 → 4.
  • Thinking a decimal is a different kind of number from a fraction. Show the same bar labelled both ways.

How to help: Spot decimals together: thermometers, race times, kilometres on a car trip display, nutrition labels. A metre stick or tape measure is a great tenths tool: every 10 cm is 0.1 m. (Money has two decimal places, so it fits better with hundredths in a later grade.)