in decimal fractions denominator is a repeated product of
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Answer:
This page is about converting a fraction (i.e. a ratio of two numbers, also called a rational number) into a decimal fraction and the patterns that occur in such a decimal fraction. It is interactive and you can use the calculators on this page to investigate fractions for yourself to many decimal places. No special knowledge beyond decimals and division is required.
Contents of this page
The Things To Do icon means there is a Things to do section of questions to start your own investigations. The calculator calculator icon indicates that there is a live interactive calculator in that section.
1 Changing a Fraction into a Decimal number
1.1 Some examples and patterns
1.2 Three types of decimal fractions
1.3 Patterns in recurring decimals
1.4 Notation for the recurring part of a decimal fraction
1.4.1 / Things to do
1.4.2 Alternative forms for some recurring fractions
1.4.3/ Things to do
1.4.4 Fraction to Decimal Calculator
2 Converting a decimal fraction into a proper fraction
2.1 Converting a terminating decimal to a fraction
2.2 Converting a periodic fraction to a fraction
2.2.1 A purely periodic decimal fraction
2.2.2 A mixed periodic decimal fraction
2.3 Decimal to Fraction Calculator
2.4 / Things to do
3 Which decimal fractions terminate and which recur?
3.1 How to tell if a fraction is terminating as a decimal fraction
3.1.1 How to find the length of a terminating decimal fraction
3.2 How to tell if a fraction is purely recurring as a decimal fraction
3.2.1 The length of the period of a purely periodic decimal fraction
3.3 Mixed Recurring Fractions
3.3.1 How long are the fixed and recurring parts of a mixed recurring fraction?
3.4 Fractions with the same denominator
3.4.1 Same denominator Decimal Fraction Calculator
3.4.2 The number of fractions with the same denominator and Euler's Totient function φ(n)
3.4.3 Nontotient Numbers
3.5 Fractions with the same lengths of period, fixed part or terminating part
3.5.1 Terminating Decimals of a given length
3.5.2 Purely periodic decimals of a given length
3.5.3 Decimals of given fixed part length and period length
3.5.4 Similar sized Decimals Calculator
3.5.5 Plots of Period lengths
4 Decimal fractions that look like special sequences
4.1 Powers of a number
4.1.1 Shift-and-add applied to the a series makes the fraction!
4.1.2/ Things to do
4.1.3 The powers backwards!
4.1.4 Series to Decimal Fraction Calculator
4.2 Summing powers in a decimal
4.2.1 / Things to do
Step-by-step explanation:
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