Finding a decimal on the number line

Where is 1.4 on the number line? It is 1 and 4 tenths: split the gap between 1 and 2 into 10 equal parts and count 4 along.

To find 4.185, zoom in step by step: between 4 and 5, then between 4.1 and 4.2, then between 4.18 and 4.19. Each zoom splits the last step into 10. Try 9.876 and 0.407.

Sonu says 0.2 can also be written 0.20 or 0.200. Zara thinks the extra zeros change the value. Who's right? Check the places: 0.2 is 2 tenths; 0.20 is 2 tenths and 0 hundredths; 0.200 is 2 tenths, 0 hundredths and 0 thousandths. All the same! Sonu is right. Zeros added at the end change nothing.

But zeros put in front of the digits change everything: 0.02 is 2 hundredths and 0.002 is 2 thousandths. So 0.2, 0.02 and 0.002 are all different, and 0.002 is the smallest. Which of these are the same number: 4.5, 4.05, 0.405, 4.050, 4.50, 4.005, 04.50?

Not every number line is marked in tenths. A line from 5 to 10 split into 10 parts has 5 units over 10 parts, so each part is half a unit. The mark 5 parts along is 7.5. Always work out what one part is worth before you read the line.