Chapter 4 of 8

All 8 chapters
  1. 1Equal fractions and simplest form, readunderstood
  2. 2Adding and taking away fractions, readunderstood
  3. 3Multiplying and dividing fractions, readunderstood
  4. 4Tenths, hundredths and thousandths, readunderstood
  5. 5Adding and taking away decimals, readunderstood
  6. 6Multiplying and dividing decimals, readunderstood
  7. 7Fractions and decimals, readunderstood
  8. 8Percentages, readunderstood

M3.3.4 Chapter 4

Tenths, hundredths and thousandths

Is 0.45 bigger than 0.5, because 45 is bigger than 5?

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

  • Say what each digit in 3.472 is worth
  • Read 3.47 and 3,47 as the same number
  • Order decimals like 0.5, 0.45 and 0.405

In a whole number, each place is ten times bigger than the place to its right. Decimals carry on the same pattern to the right. Each place is ten times smaller than the one before it.

The decimal point separates the whole numbers from the parts. The first place after it holds tenths. The next holds hundredths, and the next holds thousandths.

Here is 3.472 in a place value chart. The 3 is in the ones place, so it is worth 3. The 4 is in the tenths place, just after the point. It is worth 4 tenths.

A place value chart with the headings ones, tenths, hundredths and thousandths, and a decimal point between ones and tenths. The digits are 3, 4, 7 and 2. A row below shows what each digit is worth: 3, 0.4, 0.07 and 0.002.onestenthshundredthsthousandths347230.40.070.002
The 7 is in the hundredths place and the 2 is in the thousandths place. Each digit has its own worth.

Worked example

Say what each digit in 3.472 is worth.

  1. The 3 is in the ones place, so it is worth 3.
  2. The 4 is in the tenths place. 4 tenths is 4 ÷ 10 = 0.4.
  3. The 7 is in the hundredths place. 7 hundredths is 7 ÷ 100 = 0.07.
  4. The 2 is in the thousandths place. 2 thousandths is 2 ÷ 1 000 = 0.002.
  5. So 3.472 = 3 + 0.4 + 0.07 + 0.002.

Answer: 3, 0.4, 0.07 and 0.002

A 0 holds a place. In 3.05 there are no tenths, so the tenths place has a 0. Never leave it out. 3.5 and 3.05 are different numbers.

In some places people write a comma where others write a point. They do the same job. 3,47 and 3.47 are the same number. Where a point is used, a comma can instead split a big number into groups, as in 1,250. This book uses a point, and writes 1 250 with a small space.

Worked example

Write 3,47 with a decimal point, and say what its digits are worth.

  1. A comma and a point both separate the whole numbers from the parts.
  2. Swap the comma for a point. 3,47 becomes 3.47.
  3. The 4 is in the tenths place. It is worth 4 ÷ 10 = 0.4.
  4. The 7 is in the hundredths place. It is worth 7 ÷ 100 = 0.07.
  5. So 3,47 and 3.47 are the same number, 3 + 0.4 + 0.07.

Answer: 3.47

See it three ways

With things

Take a square made of 100 small squares. Shade 4 whole rows of 10, and then 7 more squares.

As a picture

A square grid of 100 small squares. Four whole rows are shaded with lines, and 7 more squares in the next row are shaded with dots. The caption says 47 squares.47 squares

In symbols

47 hundredths = 4 tenths + 7 hundredths = 0.47.

To compare decimals, compare the whole numbers first. If they are equal, the tenths decide. If the tenths are equal, look at the hundredths, and so on. It helps to write every number with the same number of places.

A number line from 0.40 to 0.50 with a tick for each hundredth. Three points are marked: 0.405 just after 0.40, 0.45 in the middle, and 0.5 at the right end.0.400.450.500.4050.450.5
The number line shows the order: 0.405, then 0.45, then 0.5.
A place value chart with the headings ones, tenths, hundredths and thousandths. Three rows: 0.5, 0.45 and 0.405. Missing places are filled with a 0 in a dashed box, so every row has three decimal places: 0.500, 0.450 and 0.405.onestenthshundredthsthousandths050004500405
The dashed zeros do not change a number. They let you compare place by place: 5 tenths is more than 4 tenths.

Worked example

Put 0.5, 0.45 and 0.405 in order, smallest first.

  1. Give all three the same number of places. 0.5 = 0.500 and 0.45 = 0.450.
  2. Now read them as thousandths. 0.500 is 500 thousandths, 0.450 is 450, and 0.405 is 405.
  3. Order the whole numbers. 405 is less than 450, and 450 is less than 500.
  4. So the order is 0.405, 0.45, 0.5.

Answer: 0.405, 0.45, 0.5

Try it

Shade a decimal on squared paper

You need: squared paper, a pencil.

  1. Draw a square 10 squares wide and 10 squares high. It has 100 small squares.
  2. Shade 3 whole rows of 10 with lines.
  3. Shade 5 more squares in the next row with dots.
  4. Say how many tenths and how many hundredths you shaded.

What you will see: You shaded 3 tenths and 5 hundredths. That is 35 hundredths, or 0.35.

If you cannot try it, this is what happens.
A square grid of 100 small squares. Three whole rows are shaded with lines, and 5 more squares are shaded with dots. The caption says 35 squares.35 squares

A wrong idea many people have

0.45 is bigger than 0.5, because 45 is bigger than 5.

Why it feels right: With whole numbers, a number with more digits is bigger. 45 is bigger than 5.

The test that breaks it: Write both with two places. 0.5 = 0.50. Now compare 50 hundredths with 45 hundredths. Or find them on a number line. 0.5 is to the right of 0.45.

What is true: Compare place by place from the left. 0.5 and 0.45 both have 0 ones, so look at the tenths. 0.5 has 5 tenths and 0.45 has only 4. More digits after the point does not mean a bigger number.

Key words

decimal point
the dot that separates the whole numbers from the parts, as in 3.47.
tenths
the first place after the decimal point. One tenth is 1/10.
hundredths
the second place after the point. One hundredth is 1/100.
thousandths
the third place after the point. One thousandth is 1/1000.

Back to your guess

The answer is C: No. 0.5 is bigger. It is 50 hundredths, and 0.45 is 45 hundredths.

0.5 is 5 tenths, which is 50 hundredths. 0.45 is only 45 hundredths. More digits after the point does not mean a bigger number.

Check yourself

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

  1. In 3.472, what is the 7 worth?

    Tap your answer.

    1. Not this one. 0.007 is 7 thousandths. Thousandths are the third place after the point, and the 7 is in the second. Go to M3.3.4. Try another.

    2. Not this one. You read the 7 as 7 ones. The 7 is two places after the point, in the hundredths place. Go to M3.3.4. Try another.

    3. Not this one. 0.7 is 7 tenths. The 7 is in the second place after the point, which holds hundredths. Go to M3.3.4. Try another.

    4. Yes, that is right. The 7 is in the hundredths place. 7 hundredths is 7 ÷ 100 = 0.07.

    See the answer

    0.07

    The 7 is in the hundredths place. 7 hundredths is 7 ÷ 100 = 0.07.

    • If you chose A: 0.007 is 7 thousandths. Thousandths are the third place after the point, and the 7 is in the second. Go to M3.3.4.
    • If you chose B: You read the 7 as 7 ones. The 7 is two places after the point, in the hundredths place. Go to M3.3.4.
    • If you chose C: 0.7 is 7 tenths. The 7 is in the second place after the point, which holds hundredths. Go to M3.3.4.

  2. What decimal is the dot on this number line?

    A number line from 0.30 to 0.40 with a tick for each hundredth. A dot is marked with the label ?.0.300.350.40?
    Tap your answer.

    1. Not this one. Each small step is one hundredth, not one tenth. The dot is 7 steps after 0.30, so it is 0.30 + 0.07. Go to M3.3.4. Try another.

    2. Yes, that is right. Each small step is one hundredth. The dot is 7 steps after 0.30, so it is 0.30 + 0.07 = 0.37.

    3. Not this one. 0.307 is 3 tenths and 7 thousandths. The dot is 7 hundredths after 0.30, so the 7 goes in the hundredths place. Go to M3.3.4. Try another.

    See the answer

    0.37

    Each small step is one hundredth. The dot is 7 steps after 0.30, so it is 0.30 + 0.07 = 0.37.

    • If you chose A: Each small step is one hundredth, not one tenth. The dot is 7 steps after 0.30, so it is 0.30 + 0.07. Go to M3.3.4.
    • If you chose C: 0.307 is 3 tenths and 7 thousandths. The dot is 7 hundredths after 0.30, so the 7 goes in the hundredths place. Go to M3.3.4.

  3. A scale in a shop shows 12,35 kg. Which number is that?

    Tap your answer.

    1. Yes, that is right. A comma and a point do the same job. Swap the comma for a point: 12,35 is 12.35.

    2. Not this one. You left out the comma. Here the comma does the job of the decimal point. It separates the whole numbers from the parts. Go to M3.3.4. Try another.

    3. Not this one. You added a 0 that is not there. 35 hundredths is written .35, with the 3 in the tenths place. Go to M3.3.4. Try another.

    See the answer

    12.35

    A comma and a point do the same job. Swap the comma for a point: 12,35 is 12.35.

    • If you chose B: You left out the comma. Here the comma does the job of the decimal point. It separates the whole numbers from the parts. Go to M3.3.4.
    • If you chose C: You added a 0 that is not there. 35 hundredths is written .35, with the 3 in the tenths place. Go to M3.3.4.

  4. Which is the biggest?

    Tap your answer.

    1. Not this one. It has more digits, but that does not make it bigger. 0.399 has 3 tenths and 0.4 has 4. Go to M3.3.4. Try another.

    2. Not this one. Count the tenths. 0.35 has 3 tenths, but 0.4 has 4 tenths. Go to M3.3.4. Try another.

    3. Yes, that is right. All three have 0 ones, so compare the tenths first. 0.4 has 4 tenths, and the others have only 3. So 0.4 is the biggest.

    See the answer

    0.4

    All three have 0 ones, so compare the tenths first. 0.4 has 4 tenths, and the others have only 3. So 0.4 is the biggest.

    • If you chose A: It has more digits, but that does not make it bigger. 0.399 has 3 tenths and 0.4 has 4. Go to M3.3.4.
    • If you chose B: Count the tenths. 0.35 has 3 tenths, but 0.4 has 4 tenths. Go to M3.3.4.

  5. Which list is in order, smallest first?

    Tap your answer.

    1. Not this one. 0.7 is 7 tenths, which is more than 0.07. Write both with three places: 0.700 and 0.070. Go to M3.3.4. Try another.

    2. Yes, that is right. Write them with three places. 0.070, 0.700 and 0.707. 70 is less than 700, and 700 is less than 707.

    3. Not this one. That list goes from biggest to smallest. The question asks for smallest first. Go to M3.3.4. Try another.

    See the answer

    0.07, 0.7, 0.707

    Write them with three places. 0.070, 0.700 and 0.707. 70 is less than 700, and 700 is less than 707.

    • If you chose A: 0.7 is 7 tenths, which is more than 0.07. Write both with three places: 0.700 and 0.070. Go to M3.3.4.
    • If you chose C: That list goes from biggest to smallest. The question asks for smallest first. Go to M3.3.4.

  6. In 5.073, what is the 7 worth? Write it as a decimal.

    See the answer

    0.07

    The 0 is in the tenths place and the 7 is in the hundredths place. 7 hundredths is 7 ÷ 100 = 0.07.

  7. Put these in order, smallest first. 0.6, 0.58, 0.508

    See the answer

    0.508, 0.58, 0.6

    Write them with three places. 0.600, 0.580 and 0.508. 508 is less than 580, and 580 is less than 600.

  8. A label reads 0,48. Write the number with a decimal point.

    See the answer

    0.48

    A comma and a point do the same job. Swap the comma for a point.

  9. From an earlier chapter

    Multiply. 1/2 × 3/5

    See the answer

    3/10

    1 × 3 = 3 and 2 × 5 = 10. 3/10 is already in simplest form.

Keep it

Copy this into your exercise book.

Each place to the right of the point is ten times smaller. Tenths, hundredths, thousandths. Compare place by place from the left. 3,47 is 3.47.

Draw: A chart with the headings ones, tenths, hundredths and thousandths. Write 3.472 in it.

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 (828 KB). It opens on any phone.