find out four equivatant fractions of 128/2480 using division operation.
Answers
Step-by-step explanation:
1.2 Three types of decimal fractions
In the table we can see that some decimal fractions stop after a few decimal places - those in the left-hand columns - such as 1/2, 1/4, 1/5, 1/8.
These are called terminating decimals.
But others become an endlessly repeating cycle of the same digits - those in the right-hand columns - such as 1/3, 1/6, 1/7.
These are called recurring (or repeating) decimal fractions. These recurring fractions are of two kinds:
Some decimal fractions are solely a collection of digits that repeat from the beginning, such as 0.3 which is just 3 repeating for ever and 1/7 which is 142857 endlessly repeated.
These are called purely repeating decimal fractions
Others start off with a fixed set of digits before they too eventually settle down to an endless repetition of the same digits, such as
1/6 = 0.1666666...
which begins 0.1 and then cycles 6 indefinitely
1/12 = 0.0833333...
which starts 0.08 before it too starts to repeat 3 for ever.
These are also called mixed recurring decimal fractions.
At first it is surprising that every fraction fits into one of these two categories:
The decimal fraction of every proper fraction is either terminating or else it becomes recurring.
We could simplify this even further by saying that all terminating decimals end with the infinite cycle of 000000... so that every proper fraction is a recurring decimal !
1.3 Patterns in recurring decimals
If we take all the fractions with the same denominator, that is, the lower number in a fraction, we can find some amazing patterns too. The first and simplest are the sevenths, the ninths and the elevenths:
1/7 = 0.142857 142857 142857 ...
2/7 = 0.285714 285714 285714 ...
3/7 = 0.428571 428571 428571 ...
4/7 = 0.571428 571428 571428 ...
5/7 = 0.714285 714285 714285 ...
6/7 = 0.857142 857142 857142 ... 1/9 = 0.1111111...
2/9 = 0.2222222...
3/9 = 0.3333333...
4/9 = 0.4444444...
5/9 = 0.5555555...
6/9 = 0.6666666...
7/9 = 0.7777777...
8/9 = 0.8888888... 1/11 = 0.0909090909...
2/11 = 0.1818181818...
3/11 = 0.2727272727...
4/11 = 0.3636363636...
5/11 = 0.4545454545...
6/11 = 0.5454545454...
7/11 = 0.6363636363...
8/11 = 0.7272727272...
9/11 = 0.8181818181...
10/11= 0.9090909090...
1.4 Notation for the recurring part of a decimal fraction
Mathematicians use one of two common notations to indicate which of the digits in a decimal fraction are in the repeating part: the period or cycle.
a dot is put over the first and last digits in the recurring sequence
This notation goes back at least to Robertson (1768).
a line is drawn over the repeating part
Both of these are a little awkward on web pages and as the output from computer programs and calculators, so an alternative is also used:
enclose the recurring part inside [ and ] brackets
For example:
1/7 = 0·142857 142857 14.. =
- -
0· 1 4 2 8 5 7
=
0· 142857
= 0·[142857]
3/44 = 0·06 81 81 81 81... =
- -
0· 0 6 8 1
=
0· 0 6 8 1
= 0·06[81]
11/30 = 0·3 6666666... =
-
0· 3 6
=
0· 3 6
= 0·3[6]
1833 ÷ 5000 = 0·3666 is a terminating decimal fraction
183 ÷ 500 = 0·366 is a terminating decimal fraction
9 ÷ 25 = 0·36 is a terminating decimal fraction