Question

Express the recurring decimal 1.52 as an improper fraction

Answer 1

To convert the decimal 1.52 to a fraction, just follow these steps:
Step 1: Write down the number as a fraction of one:
1.52 = 1.52
1
Step 2: Multiply both top and bottom by 10 for every number after the decimal point:
As we have 2 numbers after the decimal point, we multiply both numerator and denominator by 100. So,
1.52
1
= (1.52 × 100)
(1 × 100)
= 152
100
.
Step 3: Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(152,100) = 4. So,
(152÷4)
(100÷4)
= 38
25
when reduced to the simplest form.
As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 152
100
is also

Answer 2

(152÷4)(100÷4) = 3825 when reduced to the simplest form. As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 152100 is also equal to 11325 when expressed as a mixed number.