Convert the pure repeating (recurring) decimal number 2.34. Turn it into a reduced (simplified) improper fraction, into a mixed number and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding

Convert 2.34

1. Write the pure repeating (recurring) decimal number as a percentage.

Approximate to the desired number of decimal places (14):

2.34 ≈ 2.34343434343434

Multiply the number by ^{100}/_{100}.

The value of the number does not change when multiplying by ^{100}/_{100}.

Note: ^{100}/_{100} = 1

2.34343434343434 =

2.34343434343434 × ^{100}/_{100} =

^{(2.34343434343434 × 100)}/_{100} =

^{234.343434343434}/_{100} =

234.343434343434% ≈

234.34%

(rounded off to a maximum of 2 decimal places)

In other words:

Approximate to the desired number of decimal places...

The numerator and the denominator are coprime numbers (no common prime factors, GCF = 1). So, the fraction cannot be reduced (simplified): irreducible fraction.

4. The fraction is an improper one, rewrite it as a mixed number (mixed fraction):

A mixed number = an integer number and a proper fraction, of the same sign.

Example 1: 2 ^{1}/_{5}; Example 2: - 1 ^{3}/_{7}.

A proper fraction = the numerator is smaller than the denominator.

232 ÷ 99 = 2, remainder = 34 =>

232 = 2 × 99 + 34 =>

^{232}/_{99} =

^{(2 × 99 + 34)} / _{99} =

^{(2 × 99)} / _{99} + ^{34}/_{99} =

2 + ^{34}/_{99} =

2 ^{34}/_{99}

^{232}/_{99}: Equivalent fractions.

The above fraction cannot be reduced.

That is, it has the smallest numerator and denominator possible.

By expanding it we can build up equivalent fractions.

(Multiply the numerator & the denominator by the same number).

Learn how to turn a decimal number into a fraction and a percentage. Steps.

1. How to write the number as a percentage:

Multiply the number by 100. Then add the percent sign, %.

2. How to write the number as a fraction:

Write down the number divided by 1, as a fraction.

Turn the top number into a whole number: multiply both the top and the bottom by the same number.

Reduce (simplify) the above fraction 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.

If the fraction is an improper one, rewrite it as a mixed number (mixed fraction).

Calculate equivalent fractions. By expanding it we can build up equivalent fractions: multiply the numerator & the denominator by the same number.