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Solve the following problems: 3. Complete the following sequences: c) 9,5; 9,6; 9,7; ... up to 10,3 d) 3,31; 3,36; 3,41; 3,46; ... up to 3,66. 4. Write down three decimal numbers between 6,1 and 6,2.

Mathematics

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Here are the solutions to the problems.

3. Complete the following sequences:

Part c· 2 steps

$9,5; 9,6; 9,7; ...$ up to 10,3

  1. Identify the pattern.

    Each term increases by 0,1.

  2. Continue adding 0,1 until the term reaches 10,3.

    9,5
    9,6 (9,5+0,19,5 + 0,1)
    9,7 (9,6+0,19,6 + 0,1)
    9,8 (9,7+0,19,7 + 0,1)
    9,9 (9,8+0,19,8 + 0,1)
    10,0 (9,9+0,19,9 + 0,1)
    10,1 (10,0+0,110,0 + 0,1)
    10,2 (10,1+0,110,1 + 0,1)
    10,3 (10,2+0,110,2 + 0,1)
    The completed sequence is: 9,5;9,6;9,7;9,8;9,9;10,0;10,1;10,2;10,3\boxed{9,5; 9,6; 9,7; 9,8; 9,9; 10,0; 10,1; 10,2; 10,3}

Part d· 6 steps

$3,31; 3,36; 3,41; 3,46; ...$ up to 3,66

  1. Identify the pattern.

    Each term increases by 0,05.

  2. Continue adding 0,05 until the term reaches 3,66.

    3,31
    3,36 (3,31+0,053,31 + 0,05)
    3,41 (3,36+0,053,36 + 0,05)
    3,46 (3,41+0,053,41 + 0,05)
    3,51 (3,46+0,053,46 + 0,05)
    3,56 (3,51+0,053,51 + 0,05)
    3,61 (3,56+0,053,56 + 0,05)
    3,66 (3,61+0,053,61 + 0,05)
    The completed sequence is: 3,31;3,36;3,41;3,46;3,51;3,56;3,61;3,66\boxed{3,31; 3,36; 3,41; 3,46; 3,51; 3,56; 3,61; 3,66}

    4. Write down three decimal numbers between 6,1 and 6,2.

  3. To find numbers between 6,1 and 6,2, we can consider them as 6,10 and 6,20.

  4. Any three numbers between 6,10 and 6,20 will be correct.

    For example: 6,13;6,15;6,18\boxed{6,13; 6,15; 6,18} (Other valid answers include 6,11;6,12;6,14;6,16;6,17;6,196,11; 6,12; 6,14; 6,16; 6,17; 6,19).

    5. Look at the number line and write down the decimal numbers represented by the letters A to D.

  5. Determine the value of each small segment on the number line.

    The distance between 0 and 0,05 is divided into 5 equal segments.
    The value of each segment is 0,055=0,01\frac{0,05}{5} = 0,01.

  6. Calculate the value for each letter.

    A is 3 segments from 0. So, A=3×0,01=0,03A = 3 \times 0,01 = 0,03.
    B is 2 segments from 0,05. So, B=0,05+(2×0,01)=0,05+0,02=0,07B = 0,05 + (2 \times 0,01) = 0,05 + 0,02 = 0,07.
    C is 1 segment from 0,1. So, C=0,1+(1×0,01)=0,1+0,01=0,11C = 0,1 + (1 \times 0,01) = 0,1 + 0,01 = 0,11.
    D is 4 segments from 0,1. So, D=0,1+(4×0,01)=0,1+0,04=0,14D = 0,1 + (4 \times 0,01) = 0,1 + 0,04 = 0,14.
    The decimal numbers are:
    A: 0,03\boxed{0,03}
    B: 0,07\boxed{0,07}
    C: 0,11\boxed{0,11}
    D: 0,14\boxed{0,14}

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