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Question 3: In the number 3.26784, how many times greater is the value of the digit 2 than the value of the digit 4? Question 4: Doreen has a ribbon that is 8.4 m long. She cuts it into pieces that ar

Mathematics

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Answer

5000 times\text{5000 times}

14 pieces\text{14 pieces}

Step-by-step solution

8 steps

Here are the solutions to questions 3 and 4:

3.

  1. Determine the value of each digit in the number 3.26784.

    The digit 2 is in the tenths place, so its value is 0.2.
    The digit 4 is in the hundred-thousandths place, so its value is 0.00004.

  2. Divide the value of digit 2 by the value of digit 4 to find how many times greater it is.

    0.20.00004\frac{0.2}{0.00004}

  3. To simplify the division, multiply both the numerator and the denominator by 100,000 to remove the decimals.

    0.2×1000000.00004×100000=200004\frac{0.2 \times 100000}{0.00004 \times 100000} = \frac{20000}{4}

  4. Perform the division.

    200004=5000\frac{20000}{4} = 5000

    The value of digit 2 is 5000 times\boxed{\text{5000 times}} greater than the value of digit 4.

    4.

  5. Identify the total length of the ribbon and the length of each piece.

    Total length of ribbon =8.4= 8.4 m
    Length of each piece =0.6= 0.6 m

  6. Divide the total length of the ribbon by the length of each piece to find the number of pieces.

    8.4 m0.6 m\frac{8.4 \text{ m}}{0.6 \text{ m}}

  7. To simplify the division, multiply both the numerator and the denominator by 10 to remove the decimals.

    8.4×100.6×10=846\frac{8.4 \times 10}{0.6 \times 10} = \frac{84}{6}

  8. Perform the division.

    846=14\frac{84}{6} = 14

    Doreen got 14 pieces\boxed{\text{14 pieces}} of ribbon.

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