Chapter 3 of 8

All 8 chapters
  1. 1Centimetres and metres, readunderstood
  2. 2Millimetres and kilometres, readunderstood
  3. 3Tenths and the decimal point, readunderstood
  4. 4Grams and kilograms, readunderstood
  5. 5Millilitres and litres, readunderstood
  6. 6Telling the time, readunderstood
  7. 7How long it takes, readunderstood
  8. 8Perimeter and area, readunderstood

M2.6.3 Chapter 3

Tenths and the decimal point

My ruler says 1.5 m. Is that 1 m 5 cm?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Read 0.1 as one tenth, the same as 1/10
  • Write 1 m 50 cm as 1.5 m
  • Read 1.5 and 1,5 as the same number, written two ways

Think of 1 m cut into 10 equal parts. Each part is 10 cm.

Draw it first

Cut a metre into tenths

  1. A bar that is 1 m long. Step 1 labels it 1 m. Step 2 cuts it into 10 equal parts. Step 3 shades the first part. It is labelled one tenth, with the fraction 1/10, and = 0.1 m = 10 cm.1 m

    1 This bar is 1 m long.

  2. A bar that is 1 m long. Step 1 labels it 1 m. Step 2 cuts it into 10 equal parts. Step 3 shades the first part. It is labelled one tenth, with the fraction 1/10, and = 0.1 m = 10 cm.1 m

    2 Cut it into 10 equal parts. Each part is 10 cm.

  3. A bar that is 1 m long. Step 1 labels it 1 m. Step 2 cuts it into 10 equal parts. Step 3 shades the first part. It is labelled one tenth, with the fraction 1/10, and = 0.1 m = 10 cm.1 mone tenth110= 0.1 m = 10 cm

    3 One part is one tenth of a metre. It is 0.1 m.

One part is one tenth of the metre.

1/10 and 0.1 are two ways to write one tenth.

The dot in 0.1 is the decimal point. Digits after it are tenths.

In 1.5 m, the 1 is one whole metre. The 5 is five tenths.

A number line from 0 to 2 with 10 steps between each number. A dot sits on the fifth step after 1 and is labelled 1.5 m.0121.5 m
On the number line, 1.5 is 5 tenths past 1.

5 tenths of a metre is 50 cm. That is half a metre.

Worked example

Write 1 m 50 cm in metres, with a decimal point.

  1. 10 cm is one tenth of a metre.
  2. 50 cm is 5 lots of 10 cm. That is 5 tenths.
  3. 1 m and 5 tenths is 1.5 m.

Answer: 1.5 m

Many countries use a comma as the decimal mark.

So 1,5 and 1.5 are the same number. Use the mark your own books use.

Two boxes with an equals sign between them. The left box says 1.5 m. The right box says 1,5 m.1.5 m=1,5 m
Two ways to write the same length.

See it three ways

With things

Mark a 1 m string every 10 cm. Count 5 marks from the start. That is 50 cm.

As a picture

A bar cut into 10 equal parts. The first 5 parts are shaded. The label under it says 5 tenths of 1 m.5 tenths of 1 m

In symbols

5 tenths = 5/10 = 0.5. So 1 m 50 cm = 1.5 m.

Try it

Mark tenths on your metre string

You need: your metre string from chapter 1, a ruler, a pencil.

  1. Lay your string beside a ruler. Make a pencil mark at 10 cm.
  2. Make a mark at every 10 cm after that. You get 10 parts.
  3. Count 5 parts from the start. Measure them. You find 50 cm.
  4. Lay the string along a chair or a box. Count the parts.
  5. Say the length in tenths of a metre, like this: 0.8 m.

What you will see: Each part is one tenth of 1 m. 3 parts is 0.3 m. 7 parts is 0.7 m.

If you cannot try it, this is what happens.
A string drawn as a line with 11 marks, each 10 cm apart. A bracket over the first 5 parts is labelled 5 tenths = 0.5 m. Under the line are the labels 0, 0.5 and 1 m.5 tenths = 0.5 m00.51 m

A wrong idea many people have

1 m 5 cm is 1.5 m.

Why it feels right: The digits 1 and 5 are there. It seems you just add a dot between them.

The test that breaks it: Mark 5 cm on your marked string. Then find the 5th tenth mark. They are far apart. The 5th tenth mark is at 50 cm.

What is true: 1.5 m is 1 m 50 cm. 1 m 5 cm is a little more than 1 m. It is much less than 1.5 m.

Key words

tenth
one of 10 equal parts. We write 1/10 or 0.1.
decimal point
the dot in a number like 1.5. In many countries it is a comma.

Back to your guess

The answer is B: No. 1.5 m is 1 m and 50 cm.

The 5 after the point means 5 tenths. 5 tenths of a metre is 50 cm. So 1.5 m is 1 m 50 cm.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. Write 1 m 20 cm in metres, with a decimal point.

    See the answer

    1.2 m

    20 cm is 2 lots of 10 cm. That is 2 tenths. So 1 m 20 cm is 1.2 m.

  2. What number is the dot on?

    A number line from 0 to 1 with 10 steps. A dot sits on the seventh step after 0.01
    Tap your answer.

    1. Not this one. That is far too small. The dot is on the 7th mark. That is 7 tenths. Try another.

    2. Yes, that is right. Each step is one tenth. The dot is on the 7th step. That is 7 tenths, or 0.7.

    3. Not this one. The line only goes up to 1. The dot is 7 tenths of the way, so it is 0.7. Try another.

    See the answer

    0.7

    Each step is one tenth. The dot is on the 7th step. That is 7 tenths, or 0.7.

    • If you chose A: That is far too small. The dot is on the 7th mark. That is 7 tenths.
    • If you chose C: The line only goes up to 1. The dot is 7 tenths of the way, so it is 0.7.

  3. Which is the same as 0.1?

    Tap your answer.

    1. Not this one. Ten is a whole number. 0.1 is a small part of one. Try another.

    2. Not this one. One half is 0.5, which is five tenths. 0.1 is only one tenth. Try another.

    3. Yes, that is right. 0.1 is one tenth, the same as 1/10.

    See the answer

    one tenth

    0.1 is one tenth, the same as 1/10.

    • If you chose A: Ten is a whole number. 0.1 is a small part of one.
    • If you chose B: One half is 0.5, which is five tenths. 0.1 is only one tenth.

  4. Which is longer, 1.5 m or 1 m 5 cm?

    Tap your answer.

    1. Not this one. The .5 may look small. It means 5 tenths of a metre, which is 50 cm. 50 cm is more than 5 cm. Try another.

    2. Yes, that is right. 1.5 m is 1 m 50 cm. 50 cm is more than 5 cm.

    3. Not this one. You read 1.5 m as 1 m 5 cm. The 5 means 5 tenths, which is 50 cm. Try another.

    See the answer

    1.5 m

    1.5 m is 1 m 50 cm. 50 cm is more than 5 cm.

    • If you chose A: The .5 may look small. It means 5 tenths of a metre, which is 50 cm. 50 cm is more than 5 cm.
    • If you chose C: You read 1.5 m as 1 m 5 cm. The 5 means 5 tenths, which is 50 cm.

  5. Ana lives where a comma is the decimal mark. Her tape says 2,4 m. Write it with a point, and in m and cm.

    See the answer

    2.4 m, or 2 m 40 cm

    A comma and a point mean the same. 4 tenths of a metre is 40 cm.

  6. From an earlier chapter

    Which is longer, 1 km or 900 m?

    Tap your answer.

    1. Not this one. You compared 1 with 900. Change to the same unit first. 1 km is 1 000 m. Go to M2.6.2. Try another.

    2. Yes, that is right. 1 km is 1 000 m. 1 000 is more than 900.

    See the answer

    1 km

    1 km is 1 000 m. 1 000 is more than 900.

    • If you chose A: You compared 1 with 900. Change to the same unit first. 1 km is 1 000 m. Go to M2.6.2.

  7. Kofi cuts a 1 m string into 10 equal parts. He keeps the 4 shaded parts. How many cm is that?

    A bar cut into 10 equal parts. The first 4 parts are shaded. The label under it says 4 of the 10 parts of 1 m.4 of the 10 parts of 1 m
    Tap your answer.

    1. Yes, that is right. 1 m is 100 cm. 10 parts, so each part is 10 cm. 4 parts are 4 × 10 = 40 cm.

    2. Not this one. You counted 4 parts and called each part 1 cm. Each part is 10 cm. Try another.

    3. Not this one. You used 100 cm for each part. 100 cm is the whole string, not one part. Try another.

    See the answer

    40 cm

    1 m is 100 cm. 10 parts, so each part is 10 cm. 4 parts are 4 × 10 = 40 cm.

    • If you chose B: You counted 4 parts and called each part 1 cm. Each part is 10 cm.
    • If you chose C: You used 100 cm for each part. 100 cm is the whole string, not one part.

  8. A rope ends at the dot on the line. How long is the rope?

    A number line from 2 to 3 with 10 steps between. A dot sits on the third step after 2. A label says the numbers are metres, m.23The numbers are metres, m
    Tap your answer.

    1. Not this one. You counted the steps back from 3. Count the steps forward from 2. There are 3. Try another.

    2. Not this one. The line only runs from 2 m to 3 m. The dot is between them. So the rope is between 2 m and 3 m. Try another.

    3. Yes, that is right. The dot is 3 steps after 2. Each step is one tenth. So the rope is 2 m and 3 tenths, 2.3 m.

    See the answer

    2.3 m

    The dot is 3 steps after 2. Each step is one tenth. So the rope is 2 m and 3 tenths, 2.3 m.

    • If you chose A: You counted the steps back from 3. Count the steps forward from 2. There are 3.
    • If you chose B: The line only runs from 2 m to 3 m. The dot is between them. So the rope is between 2 m and 3 m.

Keep it

Copy this into your exercise book.

One tenth is 1/10 and 0.1. 10 tenths make 1. 1 m 50 cm is 1.5 m. 1,5 and 1.5 are the same number.

Draw: A bar for 1 m cut into 10 parts. Shade 5 and write 0.5 m.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (882 KB). It opens on any phone.