Numbers that take their value from their place

This lesson asks you to read and build whole numbers by their places, and to read, compare and order decimal numbers up to hundredths. The museum offers two records: how nine numerals and a zero give each place its value, and an early treatment of tenths and hundredths. Large whole numbers up to 100 000, comparing and ordering decimals, and everyday uses of numbers are for your class to bring. ¹

Write a number with the same digit in several places and say what each one is worth. Then break the number apart by its places and put it back together.

Look at how each place to the right is worth less than the one before it. Compare two decimal numbers place by place, starting from the largest place.

Start with 13 and halve it again and again. The historian Saidan describes the list 13, 6.5, 3.25, 1.625, 0.8125, and says the steps can be undone by multiplying by two ². The record writes the numbers with our modern dot, not as al-Uqlidisi drew them: he put a line over the units place and insisted that it be used ². Keeping the units place marked is what lets us read the places below one, instead of mistaking small parts for a large whole number ².

Each time you halve 13 the number gets smaller and needs more places. Why would a writer need to mark where the ones place is before writing 0.8125, and what could go wrong without a mark?

• al-Uqlidisi's decimal-fraction methods: the halving list and the units mark, with the historians' disagreement about them.
• Algorism: the nine numerals and the zero that give each place its value.
• al-Uqlidisi: what is known of the author, and what is not.

Read about al-Uqlidisi's decimal-fraction methods. Write a half, a quarter and a tenth of a unit as tenths and hundredths.