Question

The number 3.45' consist of a whole number and a reccuring decimal. Convert the number into an improper fraction and hence into a mixed number​.

Answer 1

To convert 3.45' into an improper fraction, multiply by a power of 10 to eliminate the recurring decimal and simplify the fraction. The improper fraction is 38/11, and the mixed number representation is 3 5/11.

Step-by-step explanation:

To convert the number 3.45' into an improper fraction, we need to understand the concept of recurring decimals. In this case, the digit 5 repeats infinitely. To represent this as an improper fraction, we can use the following steps:

1. Let x = 3.45'
2. Multiply both sides of the equation by a power of 10 that eliminates the recurring decimal.
   • Multiplying by 100 removes the recurring decimal, so 100x = 345.55'
3. Subtract the original equation from the new equation to eliminate the recurring decimal.
   • 100x - x = 345.55' - 3.45'
     99x = 342
4. Express the result as a fraction by placing the value obtained over the appropriate power of 10.
   • x = 342/99
5. Simplify the fraction if possible.
   • x = 38/11

Therefore, the number 3.45' can be represented as the improper fraction 38/11. To convert it into a mixed number, we divide the numerator (38) by the denominator (11) and express the quotient as the whole number part of the mixed number, with the remainder as the numerator of the fractional part. In this case, 38 divided by 11 is 3 with a remainder of 5, so the mixed number representation is 3 5/11.