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Solve the following math problems: 1. 1.03 6 = ? 2. Convert 72 (base 10) to binary. 3. Simplify 0.25 100 + 10 * 2.5 = ? 4. 2/3 - 1/4 = ? 5. Find the next number in the sequence: 9, 3, 1, 1/3, ...

Mathematics

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Here are the solutions to the problems:

1. Multiply 1.03×61.03 \times 6

1.03×6=6.181.03 \times 6 = 6.18

The answer is 6.18\boxed{6.18}.

2. Change 72 ten to binary base
To convert a base-10 number to binary, we repeatedly divide by 2 and record the remainders.
72÷2=3672 \div 2 = 36 remainder 0
36÷2=1836 \div 2 = 18 remainder 0
18÷2=918 \div 2 = 9 remainder 0
9÷2=49 \div 2 = 4 remainder 1
4÷2=24 \div 2 = 2 remainder 0
2÷2=12 \div 2 = 1 remainder 0
1÷2=01 \div 2 = 0 remainder 1
Reading the remainders from bottom to top gives the binary number.
The answer is 10010002\boxed{1001000_2}.

3. Simplify 0.25×100+10×2.50.25 \times 100 + 10 \times 2.5

  1. Perform the multiplications.

    0.25×100=250.25 \times 100 = 25 10×2.5=2510 \times 2.5 = 25
  2. Perform the addition.

    25+25=5025 + 25 = 50

    The answer is 50\boxed{50}.

    4. Subtract 23−14\frac{2}{3} - \frac{1}{4}

  3. Find a common denominator for 3 and 4, which is 12.

  4. Convert the fractions to have the common denominator.

    23=2×43×4=812\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} 14=1×34×3=312\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}
  5. Subtract the fractions.

    812−312=8−312=512\frac{8}{12} - \frac{3}{12} = \frac{8 - 3}{12} = \frac{5}{12}

    The answer is 512\boxed{\frac{5}{12}}.

    5. Find the next number in the sequence below: 9, 3, 1, \frac{1}{3}, \text{___}
    Observe the pattern: each term is obtained by dividing the previous term by 3.
    9÷3=39 \div 3 = 3
    3÷3=13 \div 3 = 1
    1÷3=131 \div 3 = \frac{1}{3}
    Following this pattern, the next term is:

    13÷3=13×13=19\frac{1}{3} \div 3 = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}

    The next number in the sequence is 19\boxed{\frac{1}{9}}.

    6. Write 20,015 in words
    The number 20,015 written in words is Twenty thousand fifteen.

    7. A farmer has roll of string of long [length missing], he cuts it into equal pieces, each 50 metres long. How many pieces does he get altogether?
    The total length of the roll of string is missing from the question.
    If the total length of the string roll were known (let's say LL metres), the number of pieces would be calculated by dividing the total length by the length of each piece:

    Number of pieces=Total length of stringLength of each piece\text{Number of pieces} = \frac{\text{Total length of string}}{\text{Length of each piece}} Number of pieces=L metres50 metres\text{Number of pieces} = \frac{L \text{ metres}}{50 \text{ metres}}

    Without the total length of the string, the exact number of pieces cannot be determined.

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