DECIMALS

Any unit may be divided into 10ths, 100ths, 1000ths, etc.

Any number of tenths, hundredths, thousandths, etc., of a unit is called a decimal fraction. When expressed with a decimal point, without a written denominator, it is usually called a decimal.

Thus, and .5, г and .05, ro‰ and .005, are decimal fractions, but the term decimal is usually restricted to the forms .5, .05, .005, .0005, etc.

4. In 5.55, the figure in tenths' place equals how many times the figure in hundredths' place? The figure in ones' place equals how many times the figure in tenths' place?

A decimal point is used to separate units from parts of units. It is always placed at the right of ones' place and before tenths' place.

5. What is the first place to the right of a decimal point called? the second place? the third place?

6. What is the largest decimal division of any unit? the second largest? the third largest?

In any decimal or whole number, 10 units of any place =1 unit of the next place to the left.

Show that United States money is a decimal system.

NOTATION AND NUMERATION OF DECIMALS

5 75

1. Express decimally fo, 100, 1000, 1800, 180, 1ooo.

The names of the decimal places most frequently used are given in the following table:

The number is read "nine thousand five and ninety-seven thousand four hundred eighty-nine millionths." Notice that the word and is read only between the whole number and the decimal.

2. How many places to the right of the decimal point are tenths written? hundredths? thousandths? ten-thousandths? hundred-thousandths? millionths?

=

14. .60005

15. Since .5 .50 .500, does canceling zeros from the right of a decimal change the value of the decimal?

Observe that canceling zeros from the right of a decimal really means canceling zeros from the numerator and the

Read first as given, then as if the zeros at the right of

A whole number and a decimal is called a mixed decimal This is read "50 and 625 thousandths."

15, 50.625.

In writing a decimal, one figure at the right of the decimal point expresses tenths, two figures express hundredths, three express Use as many zeros as are necessary to give hundredths two places, thousandths three places, etc.

thousandths, etc.

Thus, in writing 415 ten thousandths, use one zero, to give four places, 0415.

Write:

37. 675 ten-thousandths.

38. 16 and 75 millionths.

39. 400 and 45 thousandths.

40. 6006 and 66 ter-thousandths.

41. Seven hundred and forty-six ten-thousandths.
42. 900 and 84 millionths.

43. 8 and 17 ten-thousandths.

44. 896 and 301 hundred-thousandths.

45. One thousand and one thousandth.

46. 97 and 3 ten-thousandths.

47. 9864 millionths.

48. One million and one tenth.

49. 1830 and 11684 hundred-thousandths.

50. 429 thousand and 46 ten-thousandths.