Elementary arithmetic, with brief notices of its history... by Robert Potts.

EXEROISES.
ABSTRACT DECIMALS.
I.
1. Shew that decimal fractions are simply an extension of the
common cenary system of notation adopted in the arithmetic of whole
numbers.
2. Write fully in words the value of each figure in 321-123.
3. Define a decimal fraction, and a decimal; and explain what
notation is used to distinguish decimals from integers.
4. What are the advantages of decimal fractions over ordinary
fractions? State why decimal fractions are not always used in calculations.
5. Explain whether -067 or '068 is more nearly equal to -06748,
and express in words the error in excess or defect in each case.
II.
1. Find the sums of the following finite decimals, and express the
results in words: -
(1.) 100-1, '0001, 125-125 and 500.
(2.) '172, -06,1-0004, 20-02 and 001.
(3.) 12-4873, 124-873, 1248-73, 12487-3, 1-24873 and '124873.
(4.) 270, '072, '0001, 100-3508, 5-7764, and '12345.
(5.) '0010375, '0006875, '0008125, '0059625, '0000718, '0009282.
2. Find the sum of all the decimals which can be formed with the
digits 0, 3, 7, 9 in every possible way, all the four digits being used
in the same number.
III.
Find the differences of the following finite decimals:-02 and -002: -006 and '007: -027 and '123: 20'204 and 2-91741:
-027541 and '207514: 234-9 and '99999: -100 and -001: 214-0007 and
1000-000007: -0078125 and '00048828625.
IV.
1. Shew that any decimal is multiplied by 1000 by removing the
decimal point in the multiplicand three places towards the right.
2. Devise a rule foi the multiplication of finite decimals depend..
ing on the local value of the figures without reference to fractions.
3. Find the products of the following finite decimals:
2-5 and 3-7: -025 and 8: 1-25 and 12: 421 and -002: -01 and
100000: -00001 and 10000: 75-86425 and 10000: 3-45 and 34-5:
"000125 and 125000: -007853 and '00476: -0015625 and -00064: