Gold
Converting a fraction to a decimal
To change a fraction to a decimal, you divide the top number by the bottom number (divide the numerator by the denominator).
To convert Equation: frac{3}{8} to a decimal, we calculate to a decimal, we calculate Equation: 3 div 8.
so, Equation: frac{3}{8} u003d 0.375
Some decimals will terminate (end) like the example above, but many will not.
For example Equation: frac{2}{7} does not terminate.
Equation: frac{2}{7} u003d frac{0.2857142...}{2}
There are some fraction/decimal equivalents that you should be familiar with:
Equation: frac{1}{2} u003d 0.5
Equation: frac {1}{4} u003d 0.25
Equation: frac {3}{4} u003d 0.75
Equation: frac {1}{3} u003d 0.333333...(recurring)
Converting a decimal into a fraction
When you change a terminating decimal to a fraction, the denominator will be 10, or 100, or 1000 or… (depending on the number of decimal places).
0.5 means 'five tenths', soEquation: 0.5 u003d frac {5}{10} u003d frac {1}{2}
0.45 means '45 hundredths', so Equation: 0.45 u003d frac {45}{100} u003d frac {9}{20}
0.240 means '240 thousandths', so Equation: 0.240 u003d frac{240}{1000} u003d frac{6}{25}
To change recurring decimals to fractions:
LetEquation: m u003d 0.2222222...
Then Equation: 10m u003d 2.2222222...
Subtracting these we get:
Equation: 9m u003d 2soEquation: m u003d frac{2}{9}
Equation: 0.4444444... u003d frac{4}{9}
Equation: 0.6666666... u003d frac{6}{9} u003d frac{2}{3}
If the decimal repeats with two digits:
Equation: 100T u003d 24.242424...
Subtracting we have, Equation: 99T u003d 24
Equation: T u003d frac{24}{99}
A decimal that cannot be written as a fraction is an irrational number. Equation: pi is an example of an irrational number.
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If the prime factors of the denominator of a fraction in its simplest form are only 2 and/or 5, its decimal will terminate.
How do we know whether a fraction will give a terminating decimal? The rule is to find the prime factors of the denominator.
If the prime factors are only 2 and/or 5 the decimal will terminate.
Equation: frac{3}{20} u003d frac{3}{(2 times 2 times 5)} u003d 0.15
However if we have Equation: frac{1}{14} u003d frac{1}{(2 times 7)}this will not terminate.
Equation: frac{3}{28}
Equation: 28 u003d 2 times 2 times 7
so the decimal will not terminate. It will be a recurring decimal.
Equation: frac{7}{40}
Equation: 40 u003d 2 times 2 times 2 times 5
The prime factors of 40 consist of 2s and 5s, so the decimal will terminate.
Equation: frac{6}{125}
Equation: 125 u003d 5 times 5 times 5
The decimal will terminate.
Equation: frac{71}{120}
Equation: 120 u003d 2 times 2 times 2 times 3 times 5
There is a 3 in there, so the decimal will recur.
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Converting a fraction to a percentage
To change a fraction to a percentage multiply by Equation: 100 .
Equation: frac{7}{10} is equivalent to Equation: frac{7}{10} times 100 u003d 70
Converting a percentage to a fraction
To change a percentage to a fraction write the number as the numerator in a fraction with denominator 100.
Equation: 37 becomes Equation: frac{37}{100}
Equation: 4 becomes Equation: frac{4}{100} u003d frac{1}{25}
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Converting a decimal to a percentage
As Equation: 0.4 u003d frac{4}{10}, thenEquation: 0.4 u003d frac{40}{100} u003d 40 .
Multiply by 100. Can you see why this will work?
2.01 becomesEquation: 2.01 times 100 u003d 201 .
Converting a percentage to a decimal
As percentages are 'out of 100', to change a percentage to a decimal divide by 100.
Equation: 34 u003d frac {34}{100} u003d 0.34
Equation: 2 u003d frac {2}{100} u003d 0.02
Equation: 125 u003d frac {125}{100} u003d 1.25

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