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The place value table

The place value table

One way of depicting numbers is the place value table.

 

Here, the number is disassembled into its individual digits and their place value. The place value units are defined as ones, tens, hundreds and so forth; the denominations of each of these units are then transferred into the according columns of the place value table, which are labelled Th(thousands), H (hundreds), T (tens) and O (ones).

 

In the decimal system, each value unit is made up of 10 individual units of the next smaller value unit. For example, 1 hundred is 10 tens, since

Equally, 1 ten is made of 10 ones, since

Maybe a more relatable example for this would be picturing a money purse containing 10 1-pound coins. This would give you a single value unit of T (tens). Two purses containing 10 1-pound coins each would give you 2 value units of T (tens). One value unit of H (hundreds) would then be a bag containing 10 of those purses (10 value units of T).

The number 207 thus consists of 2H (hundreds), 0T (tens) and 7O (ones), since

Transferred into a place value table, that number looks like this:

Th

H

T

O

0

2

0

7

This depiction can be extended to also represent numbers smaller than 1. For this, we simply add some new value units to the right of the O-column. These value units are called

  • the tenth oder 110\frac{1}{10}, labelled t

  • the hundreth or 1100\frac{1}{100}, labelled h

  • the thousandth or 11000\frac{1}{1000}, labelled th.

Just like before, bundles of 10 units of the smaller value unit make up the next bigger value unit. A different way of saying this is that the step from one value unit to the next is defined by the factor 10. Note that the value unit furthest to the right is always the smallest. Therefore, 10th (thousandths) make up 1h (hundredth), and 10h (hundredths) make up 1t (tenth). 10t (tenths) in turn make up 1O (one).The extended value unit table looks like this:

Th

H

T

O

.

t

h

th

0

0

0

0

.

0

0

0

In order to represent decimal fractions, we again have to split up the number into its individual value units. For example, let’s consider the decimal fraction 1.83. This number can be split up as follows:

The number is made of 1O (ones), 8t (tenths) and 3h (hundredths). When represented in a place value table, it looks like this:

Th

H

T

O

.

t

h

th

1

.

8

3

0

As the number contains no th (thousandths) at all, we enter 0 into the according place in the table.


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