Problems from Decimal expression of rational numbers

Calculate the expression as quotient of integers of the following rational numbers:

  1. 1,742^
  2. 0,5373^
  3. 12,63408^
See development and solution

Development:

  1. According to our notation; a=17,b=1.742,m=1 and n=2. Then that corresponds to the quotient ba990=1.74217990=11566

  2. According to our notation; a=537,b=5.373,m=3 and n=1. Then that corresponds to the quotient ba9.000=5.3735379.000=403750

  3. According to our notation; a=1.263,b=1.263.408,m=2 and n=3. Then that corresponds to the quotient ba99.900=1.263.4081.26399.900=84.1436.660

Solution:

  1. 11566
  2. 403750
  3. 84.1436.660
Hide solution and development

Calculate the decimal expression and the repeating of the following rational numbers:

  1. 74
  2. 511
  3. 518
See development and solution

Development:

  1. If we do the division we obtain 74=1,75, which is the decimal expression. There is no repeating.

  2. If we do the division we obtain 511=0,454545

    So the repeating is 45 and the decimal expression is 0,45^.

  3. If we do the division we obtain 518=0,27777

    So the repeating is 7 and the decimal expression is 0,27^.

Solution:

  1. The decimal expression is 74=1,75. There is no repeating.
  2. The repeating is 45 and the decimal expression is 0,45^.
  3. The repeating is 7 and the decimal expression is 0,27^
Hide solution and development
View theory