Tenths and hundredths
Maths · Key Stage 2 · The School
The point marks the whole, not the middle
In 3.7 the point separates whole ones from parts of one. The 7 is seven tenths — seven of the ten pieces a single unit was cut into. In 3.75 the 5 is five hundredths, because each tenth was cut into ten again. Go one place further right and you have thousandths. The columns keep dividing by ten as you move right, exactly as they keep multiplying by ten going left. The point is not the middle of the number. It is the marker between wholes and parts.
Every decimal is a fraction in disguise
0.3 is 3/10. 0.03 is 3/100. 0.30 is 30/100, which cancels back to 3/10 — the same number written with an extra, harmless zero. Being able to swap between the two forms is what makes decimals easy later. They are not a new kind of number. They are a new way of writing one you already know.
Longer does not mean larger
Is 0.45 bigger than 0.5? It has more digits, so it looks bigger, and it is not. Compare column by column from the left. Both have 0 ones. Then 4 tenths against 5 tenths, and 5 tenths wins. The comparison is decided at the first column where the two numbers differ, and nothing after that point matters at all.
Line up the points, not the ends
Writing 0.5 as 0.50 makes the comparison with 0.45 obvious, because now both have two decimal places and you can read 50 hundredths against 45 hundredths. Adding a zero on the right of a decimal never changes its value, which is why this is always allowed and always safe. Money makes it concrete. £3.75 is three pounds and 75 hundredths of a pound, which is 75 pence. £3.7 and £3.70 are the same amount of money, and nobody writes the first one. Lining up the points is what a till does, and it is what you should do on paper.