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Again, in the use of decimals, it is unusual to give less than two figures.

244Again, in the use of decimals, it is unusual to give less than two figures.

244Thus 143 and 14 286 represent respectively and i ° ° to the same number of places of decimals, but the latter is obviously more exact than the former.

213In this table, unlike Table IV., amplitudes are all expressed as decimals of the mean value of the potential gradient for the corresponding season.

2012To add or subtract decimals, we must reduce them to the same denomination, i.e.

1610Expression in L and decimals of LI is usually recommended, but it depends on circumstances whether some other method may not be simpler.

145he prints a bar under the decimals; this notation first appears without any explanation in his "Lucubrationes" appended to the Constructio.

138We may take it to (say) 4 places of decimals; or we may suppose it to be taken to 1000 places.

139Thus, if we go to two places of decimals, we have as the integral series the numbers 1, 2, 4, 8,.

113For elementary work the multiplicand may come immediately after the multiplier, as in D; the last figure of each partial product then comes immediately under the corre up to the multiplication of decimals and of approximate values of numbers, is to place the first figure of the multiplier under the first figure of the multiplicand, as in E; the first figure of each partial product will then come under the corresponding figure of the multiplier.

108For elementary work the multiplicand may come immediately after the multiplier, as in D; the last figure of each partial product then comes immediately under the corre up to the multiplication of decimals and of approximate values of numbers, is to place the first figure of the multiplier under the first figure of the multiplicand, as in E; the first figure of each partial product will then come under the corresponding figure of the multiplier.

108The points of the compass might similarly be expressed by numbers in a binary scale; but the numbers would be ordinal, and the expressions would be analogous to those of decimals rather than to those of whole numbers.

94Multiply 970224 By The Year Of The Hegira, Cut Off Six Decimals From The Product, And Add 621.5774.

99Multiply 970224 By The Year Of The Hegira, Cut Off Six Decimals From The Product, And Add 621.5774.

99If there is this tendency to adopt too as a basis instead of to, the teaching of decimals might sometimes be simplified by proceeding from percentages to percentages of percentages, i.e.

83Also most fractions cannot be expressed exactly as decimals; and this is also the case for surds and logarithms, as well as for the numbers expressing certain ratios which arise out of geometrical relations.

83Thus, to divide 8 5.9 by 3.14159 2 7 to two places of decimals, we in effect divide.

83A better method is to ignore the positions of the decimal points, and multiply the numbers as if they were decimals between I and i o.

84There was, however, no development in the direction of decimals in the modern sense, and the Arabs, by whom the Hindu notation of integers was brought to Europe, mainly used the sexagesimal division in the ' " "' notation.

73This is the foundation of the use of recurring decimals; thus we can replace = s s = 1 o o /(' - 1 + 0 -)1 by .363636(=36/102 +36/ 104 +3 6 / 106), with an error (in defect) of only 36/(10 6.99).

78Taking, for example, the number 1.087678, the object is to destroy the significant figure 8 in the second place of decimals; this is effected by multiplying the number by 1- 08, that is, by subtracting from the number eight times itself advanced two places, and we thus obtain 100066376.

66Briggs also used decimals, but in a form not quite so convenient as Napier.

68For instance, .143 represents correct to 3 places of decimals, since it differs from it by less than 0005.

542, as base, and take as indices the successive decimal numbers to any particular number of places of decimals, we get a series of antilogarithms of the indices to this base.

552, as base, and take as indices the successive decimal numbers to any particular number of places of decimals, we get a series of antilogarithms of the indices to this base.

55The logarithms to base io of the first twelve numbers to 7 places of decimals are log 1 =0.0000000 log 5 log 2 = 0.3010300 log 6 log 3 =0.477 121 3 log 7 log 4 =0.6020600 log 8 The meaning of these results is that The integral part of a logarithm is called the index or characteristic, and the fractional part the mantissa.

56In actual practice, however, decimals only represent approximations, and the process has to be modified (§ 111).

43To multiply two decimals exactly, we multiply them as if the point were absent, and then insert it so that the number of figures after the point in the product shall be equal to the sum of the numbers of figures after the points in the original decimals.

44Sums and Differences of Decimals 6.7 77.

45On the other hand, in writing decimals, the sequence (of negative powers) is from left to right.

23Product of Decimals 6.8 78.

25If, for instance, the values of a and b, correct to two places of decimals, are 3 58 and 1 34, then 2 24, as the value of a - b, is not necessarily correct to two places.

25If, for instance, the values of a and b, correct to two places of decimals, are 3 58 and 1 34, then 2 24, as the value of a - b, is not necessarily correct to two places.

25to 276 places of decimals, and deduced the value of log e lo and its reciprocal M, the modulus of the Briggian system of logarithms. The value of the modulus found by Adams is Mo = 0-43429 44 81 9 03251 82765 11289 18916 60508 22 943 97 00 5 80366 65661 14453 78316 58646 4920-8870 77 47292 2 4949 33 8 43 17483 18706 106 74 47 6630-3733 64167 92871 58963 90656 92210 64662 81226 58521 27086 56867 03295 9337 0 86965 88266 88331 16360 773849 0514 28443 48666 76864 65860 85135 56148 212 34 87653 43543 43573 25 which is true certainly to 272, and probably to 273, places (Proc. Roy.

27The following are approximate values of the arm in decimals of a foot :

27The following are approximate values of the arm in decimals of a foot :

27As an arithmetical calculator he was not only wonderfully expert, but he seems to have occasionally found a positive delight in working out to an enormous number of places of decimals the result of some irksome calculation.

143.1416 is a little less than 3 + 7 - s o Recurring Decimals are a particular kind of series, which arise from the expression of a fraction as a decimal.

14They have no idea of decimals.

00He introduced the terms multinomial, trinomial, quadrinomial, &c., and considerably simplified the notation for decimals.

00Briggs's Logarithmorum chilias prima, which contains the first published table of decimal or common logarithms, is only a small octavo tract of sixteen pages, and gives the logarithms of numbers from unity to 1000 to 14 places of decimals.

00Briggs continued to labour assiduously at the calculation of logarithms, and in 1624 published his Arithmetica logarithmica, a folio work containing the logarithms of the numbers from to 20,000, and from 00,000 to ioo,000 (and in some copies to roi,000) to 14 places of decimals.

00There was thus left a gap between 20,000 and 90,000, which was filled up by Adrian Vlacq (or Ulaccus), who published at Gouda, in Holland, in 1628, a table containing the logarithms of the numbers from unity to 100,000 to ro places of decimals.

00The title of Gunter's book, which is very scarce, is Canon triangulorum, and it contains logarithmic sines and tangents for every minute of the quadrant to 7 places of decimals.

00The first logarithms to the base e were published by John Speidell in his New Logarithmes (London, 1619), which contains hYPerbolic log sines, tangents and secants for every minute of the quadrant to 5 places of decimals.

00Although the method is usually known by the names of Weddle and Hearn, it is really, in its essential features, due to Briggs, who gave in the Arithmetica logarithmica of 1624 a table of the logarithms of I + i r n up to r =9 to 15 places of decimals.

00Historical Development of Fractions and Decimals

00by commencing with centesimals instead of with decimals.

00(i) A number can be correct to so many places of decimals.

00§ 71) that the number differs from the true value by less than one-half of the unit represented by 1 in the last place of decimals.

000859 by 10 77 3141-5927 to four places of decimals.

00Carry out column addition and subtraction of numbers involving decimals.

00The first sentence is an algorithm rule often employed by students to explain how to multiply decimals.

00These are infinite decimals in which the digits are uniformly distributed.

00Children can refine their calculations making use of their ability to order decimals.

00Multiply and divide decimals mentally by 10 or 100, and integers by 1000, and explain the effect.

00In this table, unlike Table IV., amplitudes are all expressed as decimals of the mean value of the potential gradient for the corresponding season.

00On p. 8, 10.502 is multiplied by 3.216, and the result found to be 33.77443 2; and on pp. 23 and 24 occur decimals not attached to integers, viz.

00(1) he saw that a point or separatrix was quite enough to separate integers from decimals, and that no signs to indicate primes, seconds, &c., were required; (2) he used ciphers after the decimal point and preceding the first significant figure; and (3) he had no objection to a decimal standing by itself without any integer.

00Briggs also used decimals, but in a form not quite so convenient as Napier.

00he prints a bar under the decimals; this notation first appears without any explanation in his "Lucubrationes" appended to the Constructio.

00They have no idea of decimals.

00We may take it to (say) 4 places of decimals; or we may suppose it to be taken to 1000 places.

00This is the foundation of the use of recurring decimals; thus we can replace = s s = 1 o o /(' - 1 + 0 -)1 by .363636(=36/102 +36/ 104 +3 6 / 106), with an error (in defect) of only 36/(10 6.99).

00He introduced the terms multinomial, trinomial, quadrinomial, &c., and considerably simplified the notation for decimals.

00The logarithms to base io of the first twelve numbers to 7 places of decimals are log 1 =0.0000000 log 5 log 2 = 0.3010300 log 6 log 3 =0.477 121 3 log 7 log 4 =0.6020600 log 8 The meaning of these results is that The integral part of a logarithm is called the index or characteristic, and the fractional part the mantissa.

00Briggs's Logarithmorum chilias prima, which contains the first published table of decimal or common logarithms, is only a small octavo tract of sixteen pages, and gives the logarithms of numbers from unity to 1000 to 14 places of decimals.

00Briggs continued to labour assiduously at the calculation of logarithms, and in 1624 published his Arithmetica logarithmica, a folio work containing the logarithms of the numbers from to 20,000, and from 00,000 to ioo,000 (and in some copies to roi,000) to 14 places of decimals.

00There was thus left a gap between 20,000 and 90,000, which was filled up by Adrian Vlacq (or Ulaccus), who published at Gouda, in Holland, in 1628, a table containing the logarithms of the numbers from unity to 100,000 to ro places of decimals.

00The title of Gunter's book, which is very scarce, is Canon triangulorum, and it contains logarithmic sines and tangents for every minute of the quadrant to 7 places of decimals.

00The first logarithms to the base e were published by John Speidell in his New Logarithmes (London, 1619), which contains hYPerbolic log sines, tangents and secants for every minute of the quadrant to 5 places of decimals.

00John Thomson of Greenock (1782-1855) made an independent calculation of logarithms of numbers up to 120,000 to 12 places of decimals, and his table has been used to verify the errata already found in Vlacq and Briggs by Lefort (see Monthly Not.

00To construct this table Briggs, using about thirty places of decimals, extracted the square root of io fifty-four times, and thus found that the logarithm of 1.00000 00000 00000 12781 91493 20032 35 was 0.00000 00000 00000 05551 11512 31257 82702, and that for numbers of this form (i.e.

00to 276 places of decimals, and deduced the value of log e lo and its reciprocal M, the modulus of the Briggian system of logarithms. The value of the modulus found by Adams is Mo = 0-43429 44 81 9 03251 82765 11289 18916 60508 22 943 97 00 5 80366 65661 14453 78316 58646 4920-8870 77 47292 2 4949 33 8 43 17483 18706 106 74 47 6630-3733 64167 92871 58963 90656 92210 64662 81226 58521 27086 56867 03295 9337 0 86965 88266 88331 16360 773849 0514 28443 48666 76864 65860 85135 56148 212 34 87653 43543 43573 25 which is true certainly to 272, and probably to 273, places (Proc. Roy.

00Taking, for example, the number 1.087678, the object is to destroy the significant figure 8 in the second place of decimals; this is effected by multiplying the number by 1- 08, that is, by subtracting from the number eight times itself advanced two places, and we thus obtain 100066376.

00Although the method is usually known by the names of Weddle and Hearn, it is really, in its essential features, due to Briggs, who gave in the Arithmetica logarithmica of 1624 a table of the logarithms of I + i r n up to r =9 to 15 places of decimals.

00That for the conversion of a fraction into decimals (giving the complete period for all the prime numbers up to 997) is a specimen of the extraordinary love which Gauss had for long arithmetical calculations; and the amount of work gone through in the construction of the table of the number of the classes of binary quadratic forms must also have been tremendous.

00As an arithmetical calculator he was not only wonderfully expert, but he seems to have occasionally found a positive delight in working out to an enormous number of places of decimals the result of some irksome calculation.

00Sums and Differences of Decimals 6.7 77.

00Product of Decimals 6.8 78.

00Historical Development of Fractions and Decimals

00On the other hand, in writing decimals, the sequence (of negative powers) is from left to right.

00The points of the compass might similarly be expressed by numbers in a binary scale; but the numbers would be ordinal, and the expressions would be analogous to those of decimals rather than to those of whole numbers.

00If there is this tendency to adopt too as a basis instead of to, the teaching of decimals might sometimes be simplified by proceeding from percentages to percentages of percentages, i.e.

00by commencing with centesimals instead of with decimals.

00To add or subtract decimals, we must reduce them to the same denomination, i.e.

00To multiply two decimals exactly, we multiply them as if the point were absent, and then insert it so that the number of figures after the point in the product shall be equal to the sum of the numbers of figures after the points in the original decimals.

00In actual practice, however, decimals only represent approximations, and the process has to be modified (§ 111).

00There was, however, no development in the direction of decimals in the modern sense, and the Arabs, by whom the Hindu notation of integers was brought to Europe, mainly used the sexagesimal division in the ' " "' notation.

00Also most fractions cannot be expressed exactly as decimals; and this is also the case for surds and logarithms, as well as for the numbers expressing certain ratios which arise out of geometrical relations.

00(i) A number can be correct to so many places of decimals.

00§ 71) that the number differs from the true value by less than one-half of the unit represented by 1 in the last place of decimals.

00For instance, .143 represents correct to 3 places of decimals, since it differs from it by less than 0005.

00Thus 143 and 14 286 represent respectively and i Ã‚° Ã‚° to the same number of places of decimals, but the latter is obviously more exact than the former.

00Thus, if we go to two places of decimals, we have as the integral series the numbers 1, 2, 4, 8,.

00Expression in L and decimals of LI is usually recommended, but it depends on circumstances whether some other method may not be simpler.

00A better method is to ignore the positions of the decimal points, and multiply the numbers as if they were decimals between I and i o.

00Thus, to divide 8 5.9 by 3.14159 2 7 to two places of decimals, we in effect divide.

000859 by 10 77 3141-5927 to four places of decimals.

003.1416 is a little less than 3 + 7 - s o Recurring Decimals are a particular kind of series, which arise from the expression of a fraction as a decimal.

00This lets you pick half, quarter and eighth of an inch thickness without having to convert fractions to decimals.

00Counting on fingers and toes, for example, helps children learn how to count, but more in-depth concepts such as decimals and fractions can be made easier through the use of games and tools.

00Board games: Educational Learning Games carries a large selection of games designed to teach children math facts, whether it's simple geometry through the use of puzzles, word problems or decimals.

00That for the conversion of a fraction into decimals (giving the complete period for all the prime numbers up to 997) is a specimen of the extraordinary love which Gauss had for long arithmetical calculations; and the amount of work gone through in the construction of the table of the number of the classes of binary quadratic forms must also have been tremendous.

06

The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.