Half of halves

Half of the square we cut off, then half of the rest, etc. Five cuts we made in this way.

What part of the content of the original square is the content of the cut part?

Correct answer:

r =  0.9688

Step-by-step explanation:

$$\begin{gathered} q=1\mathrm{/}2={\displaystyle \frac{1}{2}}=0.5 \\ S=1 \\ {S}_1=S-q\cdot S=1-0.5\cdot 1={\displaystyle \frac{1}{2}}=0.5 \\ {S}_2=S_1-q\cdot S_1=0.5-0.5\cdot 0.5={\displaystyle \frac{1}{4}}=0.25 \\ {S}_3=S_2-q\cdot S_2=0.25-0.5\cdot 0.25={\displaystyle \frac{1}{8}}=0.125 \\ {S}_4=S_3-q\cdot S_3=0.125-0.5\cdot 0.125={\displaystyle \frac{1}{16}}=0.0625 \\ {S}_5=S_4-q\cdot S_4=0.0625-0.5\cdot 0.0625={\displaystyle \frac{1}{32}}\doteq 0.0313 \\ r=S-S_5=1-0.0313={\displaystyle \frac{31}{32}}=0.9688 \end{gathered}$$

Try another example

Related math problems and questions:

• The carpenters
  The carpenters cut the beam. Half of the cut pieces were 1 meter long, a quarter of the pieces were two meters long and the remaining 8 meters of the beam were cut into two equal parts. - What was the length of the original beam? - What part of the origin
• Pyramid cut
  We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm². Find the area of the
• Sale
  If the product twice price cut by 25%, what percentage was price cut in total?
• Three shapes
  1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle?
• Square metal sheet
  We cut out four squares of 300 mm side from a square sheet metal plate with a side of 0,7 m. Express the fraction and the percentage of waste from the square metal sheet.
• Cutting square
  From a square with a side of 30 cm, we cut the circle with the highest possible diameter. How many percents of the square content is this circle?
• Square
  Suppose the square's sides' length decreases by a 25% decrease in the content area of 28 cm². Determine the side length of the original square.
• Eq triangle minus arcs
  In an equilateral triangle with a 2cm side, the arcs of three circles are drawn from the centers at the vertices and radii 1cm. Calculate the content of the shaded part - a formation that makes up the difference between the triangle area and circular cuts
• Progression
  -12, 60, -300,1500 need next 2 numbers of pattern
• Star
  Calculate the content of the shaded part of square with side 28 cm.
• Cube cut
  In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.
• Wire
  One pull of wire is reduced its diameter by 14%. What will be the diameter of wire with diameter 19 mm over 10 pulls?
• The string
  They cut 113 cm from the string and divided the rest in a ratio of 5: 6.5: 8: 9.5. The longest part measured 38 cm. Find the original length of the string.
• Two rectangles 2
  A square of area 36 cm² is cut out to make two rectangles. A and B The area of area A to area B is 2 : 1 Find the dimensions of rectangles A and B.
• Geometric mean
  Calculate the geometric mean of numbers a=15.2 and b=25.6. Determine the mean by construction where a and b are the length of the lines.
• Square to rectangle
  What is the ratio of the area of a square of side x to the area of a rectangle of a rectangle of width 2 x and length 3
• Squares ratio
  The first square has a side length of a = 6 cm. The second square has a circumference of 6 dm. Calculate the proportions of the perimeters and the proportions of the contents of these squares? (Write the ratio in the basic form). (Perimeter = 4 * a, conte