Convert the decimal number 0.0002. Turn it into a reduced (simplified) proper fraction and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding
Convert 0.0002
1. Write the number as a percentage.
Multiply the number by 100/100
Note: 100/100 = 1
The value of the number does not change when multiplying by 100/100
0.0002 =
0.0002 × 100/100 =
(0.0002 × 100)/100 =
0.02/100 =
0.02%
In other words:
Multiply the number by 100...
... And then add the percent sign, %
0.0002 = 0.02%
2. Write the number as a proper fraction.
0.0002 can be written as a proper fraction.
The numerator is smaller than the denominator.
Write down the number divided by 1, as a fraction:
0.0002 = 0.0002/1
Turn the top number into a whole number.
Multiply both the top and the bottom by the same number.
This number is: 10,000.
1 followed by as many 0-s as the number of digits after the decimal point.
0.0002/1 =
(0.0002 × 10,000)/(1 × 10,000) =
2/10,000
3. Reduce (simplify) the fraction above: 2/10,000
(to the lowest terms, to its simplest equivalent form, irreducible).
To reduce a fraction divide the numerator and the denominator by their greatest (highest) common factor (divisor), GCF.
Factor both the numerator and the denominator (prime factorization).
In exponential notation (an):
2 is a prime number, it cannot be factored into other prime factors
10,000 = 24 × 54
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
GCF (2; 24 × 54) = 2
Divide both the numerator and the denominator by their greatest common factor, GCF.
2/10,000 =
2/(24 × 54) =
(2 ÷ 2) / ((24 × 54) ÷ 2) =
1/(23 × 54) =
1/5,000
1/5,000: Equivalent fractions.
The above fraction cannot be reduced.
That is, it has the smallest possible numerator and denominator.
By expanding it we can build up equivalent fractions.
Multiply the numerator & the denominator by the same number.
Example 1. By expanding the fraction by 3:
1/5,000 = (1 × 3)/(5,000 × 3) = 3/15,000
Example 2. By expanding the fraction by 7:
1/5,000 = (1 × 7)/(5,000 × 7) = 7/35,000
Of course, the above fractions are reducing...
... to the initial fraction: 1/5,000
:: Final answer ::
Written in 3 different ways
As a reduced (simplified) positive proper fraction:
0.0002 = 1/5,000
As a percentage:
0.0002 = 0.02%
As equivalent fractions:
0.0002 = 1/5,000 = 3/15,000 = 7/35,000
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