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What is the index form of 333556677888?

Mathematics

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15. The sum of 3,4,5,9 and 1=22. Find the sum of 1, 8, 3, 0, 0,9 and 1.

  1. Add all the given numbers.

    Sum =1+8+3+0+0+9+1= 1 + 8 + 3 + 0 + 0 + 9 + 1.

  2. Perform the addition.

    Sum =22= 22.

    22\boxed{22}

    16. If I borrowed the sum of 5000 FRS for 6 months at 4% per annum. How much will I pay as interest?

  3. Identify the principal (P), rate (R), and time (T).

    Principal (P) =5000= 5000 FRS.
    Rate (R) =4%= 4\% per annum =4100=0.04= \frac{4}{100} = 0.04.
    Time (T) =6= 6 months =612= \frac{6}{12} years =0.5= 0.5 years.

  4. Use the simple interest formula

    Interest (I) =P×R×T= P \times R \times T.

  5. Substitute the values and calculate the interest.

    I=5000×0.04×0.5I = 5000 \times 0.04 \times 0.5
    I=200×0.5I = 200 \times 0.5
    I=100I = 100 FRS.

    100 FRS\boxed{100 \text{ FRS}}

    17. The index form of 33377722 is 3373223^3 7^3 2^2. What is the index form of 333556677888?

  6. Understand the pattern from the example.

    The "index form" here means grouping identical digits and writing them as a base raised to the power of their count.
    For 33377722: three 33s (333^3), three 77s (737^3), two 22s (222^2).

  7. Apply this pattern to the number 333556677888.

    Count the occurrences of each digit:

    • Digit 3 appears 3 times →33\rightarrow 3^3
    • Digit 5 appears 2 times →52\rightarrow 5^2
    • Digit 6 appears 2 times →62\rightarrow 6^2
    • Digit 7 appears 2 times →72\rightarrow 7^2
    • Digit 8 appears 3 times →83\rightarrow 8^3
  8. Write the index form by combining these terms.

    The index form is 33526272833^3 5^2 6^2 7^2 8^3.

    3352627283\boxed{3^3 5^2 6^2 7^2 8^3}

    18. 4 decreased by 50% is 2. Decrease 45000 FRS by 8%.

  9. Calculate the amount of the decrease.

    Decrease amount =8%= 8\% of 45000.
    Decrease amount =8100×45000=8×450=3600= \frac{8}{100} \times 45000 = 8 \times 450 = 3600 FRS.

  10. Subtract the decrease amount from the original amount.

    New amount =45000−3600=41400= 45000 - 3600 = 41400 FRS.

    41400 FRS\boxed{41400 \text{ FRS}}

    19. A rectangle measures 6m by 5m. Find its area.

  11. Recall the formula for the area of a rectangle.

    Area =length×width= \text{length} \times \text{width}.

  12. Substitute the given dimensions.

    Length =6m= 6\text{m}
    Width =5m= 5\text{m}

  13. Calculate the area.

    Area =6m×5m=30m2= 6\text{m} \times 5\text{m} = 30\text{m}^2.

    30m2\boxed{30\text{m}^2}

    20. There are 80 0.25s in 20. How many 0.25s are in 16?

  14. To find how many times 0.25 is in 16, divide 16 by 0.25.

    Number of 0.250.25s =160.25= \frac{16}{0.25}.

  15. Convert the decimal to a fraction or multiply numerator and denominator by 100 to remove the decimal.

    0.25=140.25 = \frac{1}{4}.
    So, 160.25=1614=16×4\frac{16}{0.25} = \frac{16}{\frac{1}{4}} = 16 \times 4.

  16. Perform the multiplication.

    16×4=6416 \times 4 = 64.

    64\boxed{64}
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