Smaller units for exact measurement

The idea

When exact measures are required, smaller units of measurement are used; on a ruler the unit length between two consecutive numbers is divided into 10 equal parts, each one-tenth of the unit.

Two screws

Sonu’s mother is fixing a toy. Two screws look exactly the same, but only one of them fits. Looking closely, Sonu sees that one is a little longer.

How could Sonu find out exactly how long each screw is?

• Use a ruler with marks only at whole centimetres
• Use a ruler with extra marks between the centimetre marks
• We cannot tell; just compare by eye

Zoom in on the screws

Each pin shows where a screw ends. Tap the part of the ruler where the pin is. It zooms in and splits that centimetre into 10 equal parts. Then tap the mark under the pin.

Tenths of a centimetre

Between two numbers on the ruler, the unit length is split into 10 equal parts. Each part is one-tenth of a centimetre.

When exact measures are needed we use smaller units. On a ruler, the unit length between two numbers is divided into 10 equal parts, each one-tenth of the unit. A length of 2 7/10 cm is 2 cm and 7 tenths of a cm.

• Screw | Length
• Screw 1 | 2 and 7 tenths = 2 7/10 cm
• Screw 2 | 3 and 2 tenths = 3 2/10 cm

Notes

For exact measures, split the unit into 10 equal parts. Each part is one-tenth of the unit. 2 7/10 cm is 2 cm and 7 tenths of a cm.

Check yourself

On a ruler, the unit between 4 and 5 is split into 10 equal parts. A screw ends at the 3rd small mark after 4. How long is it?

Each centimetre on this ruler is split into how many equal parts?

Answer: 10

10 equal parts. Each part is one-tenth of a centimetre.

Screw 1 is 2 7/10 cm and screw 2 is 3 2/10 cm. How many tenths of a cm longer is screw 2?

Answer: 5 tenths

3 tenths to reach 3, then 2 more: 5 tenths. A difference of 5/10 cm is easy to feel when a screw must fit.

Why do we use tenths of a centimetre?

• 3 4/10 cm. The screw is past the 4 mark, so the whole part is 4. Then we count 3 small marks.
• 7/10 cm. That forgets the 4 whole centimetres. It is 4 cm and 3 tenths.
• 4 3/10 cm — correct. Yes! The screw passes the 4 mark, then 3 tenths more: 4 cm and 3 tenths.
• Because whole centimetres are too long for every object. Whole centimetres are fine for many things. We use tenths only when we need more exact measures.
• To measure more exactly than whole centimetres allow — correct. Yes. When exact measures are needed we use smaller units.
• Because every ruler must have 10 numbers. Rulers can have any numbers. The point is the small marks between them.