Converting Decimals, Percentages, and Fractions

Converting Decimals, Percentages, and Fractions

Mastering conversions between different mathematical representations is crucial when dealing with various real-world applications such as financial calculations, measurements, and more. In this article, we'll explore how to convert decimals, percentages, and fractions into each other.

Decimal to Percentage

To change a decimal to a percentage, you need to move the decimal point two places to the right and add a "%" symbol. For example, if you want to express 5 as a percentage, it would become 5%. So, 0.67 as a percentage would be 67%, and so forth.

Decimal to Fraction

Converting a decimal into a fraction involves multiplying by a power of ten until the result becomes an integer. Then, divide both numerator and denominator by this factor to get a reduced fraction. Here are some examples:

• To transform 0.5 to a fraction, you can do the following calculation step by step: 10 x 0.5 = 5; now, divide both by 5, so 10/5 = 2/1, which simplifies to just 2; finally, 2/1 equals 2.
• Similarly, 0.8 turns out to be 4/5 after dividing through by 2 twice: 2 x 0.8 = 1.6 → 2/1 = 1; 2 x 1.6 = 3.2 → 2/1 = 2; 2 x 2 = 4 → 2/1 = 2/1, which doesn't require any further reduction.

Percentage to Decimal

Changing a percentage back into its decimal form requires moving the decimal point two steps leftwards. Continuing our previous example: 67% converted to a decimal would give you 0.67.

Percentage to Fraction

To turn a percentage into a fraction, first change it into a decimal using the method mentioned above. Then, apply the division by one hundred rule to obtain a common fraction format:

Decimal   Fraction    Explanation
--------    ------     -------------------
0.8        4/5       Divide by 1,000 because there are three zeroes in 'percent', leaving us 800/1,000 = 4/5
1.2         6/5      No adjustment needed since there was only one zero in the original value ('one')

Fraction to Decimal

Finally, converting a fraction to a decimal means finding the quotient from the given fraction. This is accomplished by dividing the top number by the bottom number:

• If the answer has digits before the decimal point, place them all before the dot without rounding up or down.
• If the answer does not have any digits before the decimal point, place a leading digit of zero followed by the dot.

For instance, let's consider these fractions:

Fraction          Quotient
--------------    ---------
1                 1.0
2             \     /
       -----------    0.250000
3             \     /
       ------------    0.333333
4                 1.0

In summary, understanding decimal, percentage, and fractional relationships allows you to flexibly work across those systems, whether adding, subtracting, multiplying, or dividing numbers represented differently.