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} = 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} = frac{0.2857142...}{2}
There are some fraction/decimal equivalents that you should be familiar with:
Equation: frac{1}{2} = 0.5
Equation: frac {1}{4} = 0.25
Equation: frac {3}{4} = 0.75
Equation: frac {1}{3} = 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 = frac {5}{10} = frac {1}{2}
0.45 means '45 hundredths', so Equation: 0.45 = frac {45}{100} = frac {9}{20}
0.240 means '240 thousandths', so Equation: 0.240 = frac{240}{1000} = frac{6}{25}
To change recurring decimals to fractions:
LetEquation: m = 0.2222222...
Then Equation: 10m = 2.2222222...
Subtracting these we get:
Equation: 9m = 2soEquation: m = frac{2}{9}
Equation: 0.4444444... = frac{4}{9}
Equation: 0.6666666... = frac{6}{9} = frac{2}{3}
If the decimal repeats with two digits:
Equation: 100T = 24.242424...
Subtracting we have, Equation: 99T = 24
Equation: T = 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} = frac{3}{(2 times 2 times 5)} = 0.15
However if we have Equation: frac{1}{14} = frac{1}{(2 times 7)}this will not terminate.
Equation: frac{3}{28}
Equation: 28 = 2 times 2 times 7
So the decimal will not terminate. It will be a recurring decimal.
Equation: frac{7}{40}
Equation: 40 = 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 = 5 times 5 times 5
The decimal will terminate.
Equation: frac{71}{120}
Equation: 120 = 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 = 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} = frac{1}{25}
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Converting a decimal to a percentage
As Equation: 0.4 = frac{4}{10}, thenEquation: 0.4 = frac{40}{100} = 40%.
Multiply by 100. Can you see why this will work?
2.01 becomesEquation: 2.01 times 100 = 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% = frac {34}{100} = 0.34
Equation: 2% = frac {2}{100} = 0.02
Equation: 125% = frac {125}{100} = 1.25