Expressing 5.347 as p/q

To express 5.347 as p/q, we need to understand the concept of decimals and fractions. Decimals are a way of expressing fractions in a decimal form, with the denominator being a power of 10. In this case, we have a decimal number with a decimal point followed by three digits.

Step 1: Identifying the denominator

The first step to express 5.347 as a fraction is to identify the denominator. The denominator in this case will be a power of 10, which is determined by the number of digits after the decimal point. In this case, we have three digits after the decimal point, so the denominator will be 10^3, which is 1000.

Step 2: Multiplying numerator and denominator by a suitable factor

Next, we need to multiply both the numerator and denominator by a suitable factor to eliminate the decimal point. We can do this by multiplying both by 1000, which is the denominator we identified in step 1.

5.347 x 1000 = 5347
1000 x 1 = 1000

Therefore, we have 5347/1000 as the fraction equivalent of 5.347.

Simplifying the fraction

To simplify the fraction, we need to divide both the numerator and denominator by their common factors. In this case, both 5347 and 1000 can be divided by 347.

5347/347 = 15
1000/347 = 2.88

Therefore, we have 5.347 expressed as 15/2.88.

Conclusion

Thus, we can express 5.347 as p/q, where p = 15 and q = 2.88. However, q needs to be an integer, so we need to multiply both p and q by a suitable factor to eliminate the decimal point in q. We can multiply both by 100 to get p = 1500 and q = 288, which gives us the final answer of 5.347 as 1500/288.