31. Read the following, and notice the effect of moving the decimal point one, two, three, or more places to the right:

.4862; 4.862; 48.62; 486.2; 4862.

32. Read the following, and notice the effect of placing one, two, three, or more zeros between the decimal point and the first decimal figure:

26.4; 26.04; 26.004; 26.0004; 26.00004.

33. Read the following, and notice the effect of placing zeros on both sides of the decimal point:

3.3; 30.03; 300.003; 3000.0003.

34. Read the following, and notice the similarity of sound and difference of value:

404000; 400.004; .404; 303000; 300.003; .303.

NOTATION OF DECIMALS.

92. In writing a decimal, write the numerator as a whole number, and then place the decimal point so that the right-hand figure expresses the denomination required.

Write in figures—

1. Four tenths. Six tenths. Nine tenths. 2. Five hundredths. Forty-five hundredths. 3. Seven thousandths. Seventy-five thousandths. 4. Eighty-five hundredths. Eight, and five tenths. 5. Sixty, and six hundredths. 125 thousandths. 6. Three hundred and four ten-thousandths. 7. Five, and fifteen thousandths. One millionth. 8. Ninety, and nine hundredths. Four millionths. 9. One hundred and twenty, and four millionths. 10. Sixty-five hundred, and sixty-five hundredths. 11. Seventy-five thousand, and seventy-five thousandths.

12. Three hundred, and three thousandths.
13. Three hundred and three thousandths.
14. Eight tens. Eight units. Eight tenths.
15. Four hundred.
16. Six thousand.

Four tens. Four tenths.

Six thousandths.

17. Twenty-five tens. Twenty-five tenths.

18. Twenty-five hundred. Twenty-five hundredths. 19. 325 hundredths. 325 tenths.

20. 125 ten-thousandths. 125 millionths.

21. 4211 hundredths. 4211 thousandths. 22. 16, and 25 thousandths.

23. 9, and 9 ten-millionths.

24. 1007 millionths.

14 ten-millionths.

25. Four and one-half tenths.

26. Twenty-four and two-thirds hundredths.. 27. One-half tenth. One-third hundredth.

93. Principles.-1. Annexing ciphers to a decimal does not

2. Prefixing ciphers to a decimal diminishes its value ten times for every cipher prefixed.

Hence the value is diminished ten times for each cipher prefixed.

3. Moving the decimal point to the right increases the value of the decimal ten times for every place passed over.

Hence the value is increased ten times for each place passed over.

4. Moving the decimal point to the left diminishes the value of the decimal ten times for every place passed over.

Take as an example 33.3 333.

33.3 becomes 3.33 =
33.3 becomes .333

=

100

33 by moving the decimal point one place. 333 by moving it two places, etc.

1000

Hence the value is diminished ten times for each place passed over.

REDUCTION OF DECIMALS.

CASE I.

94. To reduce a decimal to a common fraction.

Express the decimal as a common fraction, and reduce it to its

lowest terms.

95. To reduce a common fraction to a decimal.

WRITTEN EXERCISES.

1. Reduce to a decimal.

PROCESS.

8)3.000

.375, Ans.

equals of 3.

3 equals 30 tenths; of 30 tenths is 3 tenths, and 6 tenths remaining; 6 tenths equals 60 hundredths; of 60 hundredths is 7 hundredths, and 4 hundredths remaining; 4 hundredths equals 40 thousandths; of 40 thousandths is 5 thousandths. Hence equals .375.

RULE.

Annex ciphers to the numerator and divide by the denominator; point off as many decimal places as there are ciphers annexed.

4.26

12.005

126.4

142.665

Add

We write the numbers so that their decimal points are in the same vertical column, and add as in whole numbers, placing the decimal point between units and tenths.

8. 4.81 +123.478 + 120.042 + 75.4 9. 63.45 + 2.3 +74.6 + 62.04 10. 100.027 + 52.67 + 634.842 + 4.7 11. 53.2 + 40.732 + 3.5 + 432.683