12-Representations-of-Numbers-4UP

12-Representations-of-Numbers-4UP - Decimal representations...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Decimal representations Alternative bases Conversions Representations of Numbers Dhavide Aruliah UOIT MATH 2070U c ± D. Aruliah (UOIT) Representations of Numbers MATH 2070U 1 / 26 Decimal representations Alternative bases Conversions Representations of Numbers 1 Decimal representations of numbers 2 Alternative representations of number with other bases 3 Conversion between numeric representations c ± D. Aruliah (UOIT) Representations of Numbers MATH 2070U 2 / 26 Decimal representations Alternative bases Conversions Decimal representations of numbers Recall: 71.32 actually means 7 1 . 3 2 = 7 × 10 + 1 × 1 + 3 10 + 2 100 = 7 × 10 1 + 1 × 10 0 + 3 × 10 - 1 + 2 × 10 - 2 7 tens + 1 unit + 3 tenths + 2 one hundredths Decimal point separates integer part from fractional part Decimal system favoured by most modern humans c ± D. Aruliah (UOIT) Representations of Numbers MATH 2070U 4 / 26 Decimal representations Alternative bases Conversions Relevance of representations XLIII × XXXVII MDXCI 43 × 37 301 1290 1591 c ± D. Aruliah (UOIT) Representations of Numbers MATH 2070U 5 / 26
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Decimal representations Alternative bases Conversions Rational numbers Rational numbers : ratio of two integers (fractions) e.g., 1 3 , 2 5 , 1 4 , - 21 137 , . . . Q R denotes set of all rational numbers Decimal representations: finite or repeating 1 4 = 0.25 = 2 × 10 - 1 + 5 × 10 - 2 2 5 = 0.4 = 4 × 10 - 1 1 3 = 0. 3 = 0. 333 ··· = 3 × 10 - 1 + 3 × 10 - 2 + 3 × 10 - 3 + ··· = k = 1 3 × 10 - k = 3 10 k = 0 ± 1 10 ² k = 3 10 ± 1 1 - 1/10 ² c ± D. Aruliah (UOIT) Representations of Numbers MATH 2070U 6 / 26 Decimal representations Alternative bases Conversions Irrational numbers Irrational numbers : real numbers not expressible as ratios 3 2 = 4.24264068711929 ··· , π = 3.14159265358979 ··· , e = 2.71828182845905 ··· , etc. Irrational numbers not finitely representable in decimal form Computer decimal representations of numbers have to be approximate c ± D. Aruliah (UOIT) Representations of Numbers MATH 2070U 7 / 26 Decimal representations Alternative bases Conversions Alternative number bases Not restricted to decimal (base 10) representations Different civilisations have used different number bases
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/23/2010 for the course MATH 2070 taught by Professor Aruliahdhavidhe during the Spring '10 term at UOIT.

Page1 / 5

12-Representations-of-Numbers-4UP - Decimal representations...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online