Different Form, Same Spot

Three quarters. Zero point seven five. Seventy-five per cent. They sound different, and they look different... but on a number line, they all land on ONE exact spot. How can three labels share one place? Let's uncover the link!

A number line arranges amounts from smaller to larger. Zero begins this line, and one whole ends it. When different forms describe the SAME amount, their position cannot change. The writing changes, but the distance from zero stays exactly the same. Suppose the line is split into four equal intervals. Three equal jumps from zero reach three quarters. The word equal matters. If the gaps have different widths, they do not represent equal fractional parts, so you cannot count them as quarters. Three quarters is seventy-five hundredths, which is zero point seven five. To change that decimal into a percentage, multiply by one hundred. You get seventy-five per cent. Never just add a percent sign - per cent means out of one hundred, so the SCALE must change too.

Try this eleven-plus question. A number line runs from zero to one and is divided into twenty equal intervals. Where should thirty-five per cent be placed? A movable marker waits at zero. We need to find its exact destination. Thirty-five per cent means thirty-five out of one hundred. Write that as thirty-five hundredths. Now simplify by dividing both numbers by five. Thirty-five hundredths becomes seven twentieths. Perfect - the line is already split into twenty equal intervals. Seven twentieths means seven of those twenty equal jumps from zero. Count carefully: one, two, three, four, five, six, seven. Stop there. The seventh tick is the location of thirty-five per cent. The marker locks onto that point. Let's check. Thirty-five per cent as a decimal is zero point three five. That is a little more than zero point three and less than zero point four. Our seventh tick sits exactly there... so the location is CORRECT.

Different form, same amount, same spot. Make sure the intervals are equal, convert the value carefully, then count equal jumps from zero. Fraction, decimal, or percentage - you now know how to pin it precisely on the number line!