Decimals and Fractions Together

You met fractions in Year 3 and decimals in the last lesson, and here is the thing worth knowing: they are the same idea in different handwriting. Seven tenths can be written 7/10 or 0.7, and the grid shows why — seven of the ten columns are shaded either way. A decimal is nothing more than a fraction whose bottom number is 10 or 100, written using place-value columns instead of a fraction bar.

The same grid handles hundredths. Cut the whole square into 100 little squares and each one is a hundredth, 0.01. Shade 23 of them and you have 23/100, which is 0.23. Look carefully at the shading: it fills two complete columns and three extra squares. Two full columns are two tenths, and the three leftovers are three hundredths — which is exactly what 0.23 says, digit by digit.

Some conversions come up so often they are worth knowing by heart. A half is 0.5, because half of ten tenths is five tenths. A quarter is 0.25, because a quarter of the hundred squares is 25 of them, and three quarters is 0.75. A tenth is 0.1, a fifth is 0.2 because a fifth of ten is two, and a hundredth is 0.01. Six facts, and they turn most decimal questions into something you can answer without working.

There is a simple rule for going from a fraction to a decimal when the bottom is 10 or 100: count the zeros on the bottom, and that is how many decimal places you need. So 6/10 has one zero and becomes 0.6. But 6/100 has two zeros and needs two places, so it is 0.06 — you have to put a zero in the tenths column to push the 6 into hundredths. And 64/100 also needs two places, giving 0.64, which fills both neatly.

Put both on a number line and the connection becomes obvious: they are labels for the same points. A quarter and 0.25 are the same spot. A half and 0.5 are the same spot. That is what lets you compare a fraction against a decimal — convert one into the other and the answer falls out. Asked whether 3/4 or 0.7 is bigger, turn 3/4 into 0.75 and it is settled immediately.