Lesson Guide
Explanation
You already know the columns to the right of the decimal point: tenths, then hundredths. There is nothing to stop you going further. One more step right and each piece is ten times smaller again — thousandths. So in 0.473, the 4 is four tenths, the 7 is seven hundredths, and the 3 is three thousandths. The pattern never changes: every step right divides by ten.
Your Turn
In the number 0.826, what is the 6 worth? Check: six thousandths.
Watch Out
Reading 0.473 as four hundred and seventy-three is a common slip. It is less than one — read the columns, not the digits.
Explanation
It helps to feel how small a thousandth actually is. Take one metre. A tenth of it is 10 centimetres, about the width of your hand. A hundredth is 1 centimetre, about a fingernail. A thousandth is 1 millimetre — the thickness of a pencil line. That is why thousandths turn up in careful measuring, in science, and in sport timing, where a race can be won by 0.003 of a second.
Your Turn
How many millimetres are in 0.007 metres? Check: 7 millimetres, because each thousandth of a metre is 1 mm.
Watch Out
A thousandth is tiny, but it is not nothing. In a close race it decides who wins.
Explanation
Here is the question that catches almost everybody: is 0.4 bigger than 0.375? It looks smaller because it has fewer digits, and that is exactly the trap. Fill the shorter one with zeros so both have three places: 0.400 against 0.375. Adding zeros on the end of a decimal changes nothing at all — four tenths is the same as four hundred thousandths. Now compare from the left: 4 tenths beats 3 tenths, so 0.4 wins.
Your Turn
Which is bigger, 0.62 or 0.618? Fill with a zero first. Check: 0.620 against 0.618, so 0.62 is bigger.
Watch Out
More digits does NOT mean bigger. 0.375 has more digits than 0.4 and is smaller.
Explanation
Every decimal is a fraction wearing different clothes, and with three places the pattern is easy to see: count the decimal places and count the zeros. One place is tenths, so 0.7 is 7/10. Two places is hundredths, so 0.07 is 7/100. Three places is thousandths, so 0.007 is 7/1000. The number of decimal places always matches the number of zeros in the bottom of the fraction.
Your Turn
Write 0.045 as a fraction. Check: three decimal places means thousandths, so 45/1000.
Watch Out
0.7 and 0.07 look almost identical and differ by ten times. Read carefully — the zero matters enormously.
Explanation
Three decimal places is often more precision than anyone needs, so you round. To round 3.478 to two places, look at the digit just after the place you are keeping — the thousandths digit, which is 8. Five or more rounds up, less than five rounds down. Eight is five or more, so the 7 becomes 8 and you get 3.48. The digit you look at is always the very next one; the ones beyond it do not get a vote.
Your Turn
Round 0.256 and 0.253 to two decimal places. Check: 0.26 and 0.25.
Watch Out
Only the NEXT digit decides. When rounding 3.4749 to two places you look at the 4, not the 9, so it stays 3.47.
📌 Key Points — this lesson in a nutshell
- Each step right divides by ten: tenths, hundredths, thousandths.
- A thousandth of a metre is 1 millimetre — small, but not nothing.
- To compare, fill with zeros so both have the same number of places.
- More digits does not mean bigger: 0.4 beats 0.375.
- Decimal places match the zeros: 3 places → over 1000.
- To round, look only at the very next digit. 5 or more rounds up.
Step 1: Introduction
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