Year 6NumberRational numbersYear 6 Maths

Tenths, hundredths and thousandths

What this lesson covers

  • Thousandths can be created by dividing whole numbers by 1,000 and can be expressed as fractions or decimals.
  • Equivalent fractions can be generated and simplified using common factors.
Key idea

There is a thousandth in your pencil case

  • Take a metre. Cut it into ten equal pieces.
  • Each piece is 10 cm: one tenth of a metre.
  • Keep cutting and you reach the smallest mark on your ruler.
There is a thousandth in your pencil case
Key idea

One whole, ten equal parts

  • Ten equal parts means each one is a tenth.
  • As a fraction that is 1/10. As a decimal, 0.1.
  • Same amount. Two ways of writing it.
One whole, ten equal parts
Key idea

Cut each tenth into ten again

  • Ten tenths, each split into ten, gives one hundred parts.
  • One of them is 1/100, or 0.01.
  • On a metre, that is one centimetre.
Cut each tenth into ten again
Key idea

Once more, and you have thousandths

  • Split each hundredth into ten. Now there are a thousand.
  • One of them is 1/1000, or 0.001.
  • On a metre, that is one millimetre. A thousand of them fit.
Once more, and you have thousandths
Key idea

Every column has a name

  • To the right of the point: tenths, then hundredths, then thousandths.
  • Each column is worth ten times less than the one before it.
  • The column a digit sits in tells you what it is worth.
Every column has a name
Worked example

Reading 0.135

  • The 1 is in the tenths column: one tenth.
  • The 3 is in the hundredths column: three hundredths.
  • The 5 is in the thousandths column: five thousandths.
  • Altogether, 135 thousandths.
Reading 0.135
Worked example

Writing seven hundredths

  • Seven hundredths means a 7 in the hundredths column.
  • The tenths column has nothing in it, so it gets a zero.
  • That zero is doing a job: it holds the 7 in place.
  • Seven hundredths is 0.07, not 0.7.
Writing seven hundredths
Key idea

The same amount, fewer pieces

  • 4/10 of the bar is shaded.
  • 4 and 10 share a common factor of 2.
  • Divide both by 2 and you get 2/5.
  • The shading has not moved. Only the names changed.
The same amount, fewer pieces
Worked example

Simplifying 6/10

  • What goes into both 6 and 10? Two does.
  • 6 ÷ 2 = 3, and 10 ÷ 2 = 5.
  • So 6/10 is 3/5.
  • Nothing goes into 3 and 5 now, so that is as simple as it gets.
Simplifying 6/10
Key idea

Per cent means per hundred

  • This grid has one hundred squares. 31 are shaded.
  • As a fraction, 31/100. As a decimal, 0.31.
  • As a percentage, 31%.
  • Three names for one amount.
Per cent means per hundred
Key idea

Worth knowing by heart: one half

  • Half of the bar is shaded.
  • 1/2 is 0.5, which is 50%.
  • You should not have to work this one out.
Worth knowing by heart: one half
Key idea

Quarters

  • 1/4 is 0.25, or 25%.
  • 3/4 is 0.75, or 75%.
  • Two quarters is a half, so 0.5 sits between them.
Quarters
Key idea

Fifths go up in twos

  • 1/5 is 0.2. 2/5 is 0.4.
  • 3/5 is 0.6. 4/5 is 0.8.
  • Every fifth adds another two tenths. That is the whole pattern.
Fifths go up in twos
Key idea

Which is bigger: 0.38 or 0.4?

  • Thirty-eight is a bigger number than four.
  • So 0.38 must be bigger than 0.4.
  • That argument is wrong, and it is worth knowing exactly why.
Key idea

Put them on a number line

  • The digits after the point are not a whole number.
  • 0.4 is four tenths. 0.38 is not even four tenths yet.
  • 0.375 is smaller still, however many digits it has.
  • Further right means bigger. The line does not care how long a number looks.
Put them on a number line
Key idea

Give them the same number of places

  • Writing 0.4 as 0.400 does not change it.
  • The extra zeros add no tenths, hundredths or thousandths.
  • Now compare 0.400, 0.380 and 0.375 (all thousandths).
  • 400, 380, 375. Now the digits can be trusted.
Give them the same number of places
Worked example

Multiplying by ten

  • 1.3 × 10. Every digit becomes worth ten times more.
  • The 1 was ones and becomes tens. The 3 was tenths and becomes ones.
  • So 1.3 × 10 = 13.
  • The digits did not change. They moved up a column.
Multiplying by ten
Worked example

Dividing by a hundred

  • 13 ÷ 100. Now every digit is worth a hundred times less.
  • The 1 drops from tens to tenths, and the 3 from ones to hundredths.
  • So 13 ÷ 100 = 0.13.
  • Two columns down, because a hundred is two tens.
Dividing by a hundred
Your turn

Four to try

  • 1. Write 9/100 as a decimal.
  • 2. Simplify 8/10.
  • 3. Put these in order, smallest first: 0.6, 0.58, 0.605.
  • 4. What is 2.4 ÷ 10?
Show answer

Answers: 1. 0.09; watch for 0.9, which is the placeholder-zero mistake from the "writing seven hundredths" beat. 2. 4/5 (divide both by 2). 3. 0.58, 0.6, 0.605. This is the trap beat again; ask for the same number of places first (0.580, 0.600, 0.605). 4. 0.24. Ask which column each digit moved to rather than accepting "move the point".

Summary

Fraction, decimal, percentage

  • The seven worth knowing without thinking.
  • Same amount, three names each.

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