Tenths: parts of one

Brief

This lesson asks you to read, compare and order decimal tenths, and to show how tenths and fractions match. The museum offers one record on early work with decimal fractions; your class brings the number lines, models and practice. ¹

How can one number be written in two ways?

Look for a fraction and a decimal tenth that name the same amount. Explain how you know they are equal.

Go deeper

Picture a strip of paper cut into ten equal pieces: five of them make a half. Cut it into a hundred pieces and twenty-five make a quarter. Today we write 0.5 and 0.25, but our signs are modern, not a manuscript imitation ². Al-Uqlidisi wrote a book at Damascus with an early, direct treatment of such fractions ³ ². The idea that matters is that a digit's position tells us which part we count, and a mark for the units place protects that reading ².

Think about it

On a strip cut into ten pieces, a half is five tenths. Why can the same strip not show a quarter as a whole number of tenths, and what would you do to show it?

Into the museum

al-Uqlidisi's decimal-fraction methods: how halving and a mark for the units place work.
al-Uqlidisi: what is known of the author, and what is not.
Algorism: the Indian place-value arithmetic his book builds on.

Try this

Read the record Al-Uqlidisi's decimal-fraction methods. Write a half and half of a half as tenths and hundredths.

At a glance

Curriculum expectations