# Converting Decimals, Percentages, and Fractions

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## 10 Questions

25%

0.75

0.85

### When converting 2.4 to a fraction, which of the following is the correct form?

$\frac{12}{5}$

0.7

1/2

0.75

0.875

240%

-1/6

## 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 = 1.62/1 = 1; 2 x 1.6 = 3.22/1 = 2; 2 x 2 = 42/1 = 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.

Learn how to seamlessly convert decimals, percentages, and fractions into each other for practical applications in finance, measurements, and more. Explore the steps involved in converting decimal to percentage, decimal to fraction, percentage to decimal, percentage to fraction, and fraction to decimal.

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