The same cut, once more
Cutting every tenth into ten equal pieces made hundredths. Between 0.1 and 0.2 there are ten hundredths: 0.11, 0.12, 0.13, up to 0.19.
the tenth from 0.1 to 0.2 holds ten hundredths, and every number inside it is < 0.2, however large its last digit looks: 0.15 = 15/100 < 20/100
Find 0.12 between 0.1 and 0.2
The tenth from 0.1 to 0.2 is drawn again underneath, cut into ten hundredths. Move the marker to 0.12.
There is still room between 0.12 and 0.13. Cut that hundredth into ten equal pieces, and each piece is a thousandth. The marks between them are 0.121, 0.122, 0.123, up to 0.129, and the one in the middle is 0.125.
A whole is 10 tenths, each tenth is 10 hundredths, and each hundredth is 10 thousandths. So a whole holds 10 × 10 × 10 = 1000 thousandths.
The hundredth from 0.12 to 0.13, cut into ten thousandths. 0.125 is the fifth mark along, halfway.
The third place after the point
Thousandths are written in the third place after the decimal point. In 0.125, the 1 counts tenths, the 2 counts hundredths and the 5 counts thousandths.
To read it as one number, read the digits without the point and name the last place: 0.125 is 125 thousandths, or . It is 125 of the 1000 equal pieces in one whole.
From 0.1 to 0.2 in hundredths. 0.125 is 1 tenth, 2 hundredths and 5 thousandths, so it lies halfway between 0.12 and 0.13.
Money stops; a length can go on
A cent is one hundredth of a dollar, and there is no coin smaller than a cent. So an amount of money such as $1.25 stops at two places after the point.
A length can be cut as finely as the ruler allows. A meter stick is marked in millimeters, and 1000 millimeters make a meter, so each millimeter is a thousandth of a meter. A height of 1.253 m is 1 meter and 253 millimeters. A finer measuring tool could go on to a fourth place.
Between 1.25 m and 1.26 m a meter stick has ten millimeter marks. The third one is 1.253 m.
More digits is not more
Each place is worth less than the place before it, so a digit in the thousandths counts very little. 0.4 is bigger than 0.375: 0.4 is 4 tenths, and 0.375 has only 3 tenths. Written with three places, 0.4 is 0.400, and 400 thousandths is more than 375 thousandths.
Name a digit by its place, counted from the point. In 0.125, the 5 is third after the point, so it counts thousandths. The 1 is first after the point, so it counts tenths.