189/40 as a Decimal and Mixed Number

189/40 as a decimal and mixed number expansion provides the detailed information about what is 189/40 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

189/40 as a Decimal
189/40 = 4.725
Hence,
189/40 as a decimal equals to 4.725
where,
189/40 is a given fraction,
The decimal expansion of 189/40 is 4.725

189/40 as a Mixed Number
189/40 = (160 + 29)/40
= 160/40 + 29/40
= 4 + 29/40
= 4 29/40
189/40 = 4 29/40

Hence,
189/40 as a mixed number is 4 ²⁹/₄₀
where,
189/40 is a given fraction,
4 ²⁹/₄₀ is the mixed number representation of 189/40.

The below work with steps provide the detailed information about how to convert fraction 189/40 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 189/40

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 189/40.

step 2 The numerator is greater than the denominator of the fraction 189/40, so write the given fraction in the expression form in terms of denominator as like the below:
= 189/40
= 160 + 29/40
= (4 x 40) + 29/40

step 3 Make the above expression as individual fractions:
= (4 x 40)/40 + 29/40

step 4 Simplify the above expression:
= 4 x 40/40 + 29/40
= 4 + 29/40
4 + 29/40 can be written as a mixed number 4 ²⁹/₄₀.


step 5 Find the decimal equivalent for the fractional part 29/40 in the above expression:
Multiply both numerator and denominator by 25 to make the denominator as powers of 10:
= 4 + (29/40 x 25/25)
= 4 + 725/1000

step 6 Simplify the above expression further:
= 4 + 0.725
= 4.725
189/40 = 4.725

Hence,
189/40 as a decimal is 4.725
189/40 as a mixed number is 4 ²⁹/₄₀