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Round-off 108.76 to the nearest tens. Write sqrt(60) correct to four significant figures. You may use a calculator or a square-roots table of values. Evaluate and write your answer correct to two significant figures: 72+43= Estimate the product: 23.8 x 349

Mathematics

ScanSolve AI Answer

Answer

110\mathbf{110}

7.746\mathbf{7.746}

6000\mathbf{6000}

Step-by-step solution

11 steps

1. Round-off 108.76 to the nearest tens.

  1. Identify the tens digit.

    In the number 108.76, the tens digit is 0.

  2. Look at the digit to the right of the tens digit.

    The digit to the right of 0 is 8 (in the ones place).

  3. Round based on the digit to the right.

    Since 8 is 5 or greater, round up the tens digit. The 0 becomes 1. All digits to the right of the tens place (before the decimal) become 0, and digits after the decimal are dropped.

    108.76≈110108.76 \approx 110

    The number rounded to the nearest tens is 110\boxed{\mathbf{110}}.

    2. Write 60\sqrt{60} correct to four significant figures.

  4. Calculate the value of 60\sqrt{60}.

    Using a calculator, 60≈7.74596669...\sqrt{60} \approx 7.74596669...

  5. Round the value to four significant figures.

    The first four significant figures are 7, 7, 4, 5. The fifth significant figure is 9, which is 5 or greater, so we round up the fourth significant figure (5).

    7.7459...≈7.7467.7459... \approx 7.746

    60\sqrt{60} correct to four significant figures is 7.746\boxed{\mathbf{7.746}}.

    3. Evaluate 72+437^2 + 4^3 and write your answer correct to two significant figures.

  6. Calculate 727^2.

    72=7×7=497^2 = 7 \times 7 = 49
  7. Calculate 434^3.

    43=4×4×4=16×4=644^3 = 4 \times 4 \times 4 = 16 \times 4 = 64
  8. Add the results.

    49+64=11349 + 64 = 113
  9. Round the sum to two significant figures.

    The first two significant figures are 1 and 1. The third significant figure is 3, which is less than 5, so we keep the second significant figure as it is and replace the remaining digits before the decimal with zeros.

    113≈110113 \approx 110

    The evaluated expression correct to two significant figures is 110\boxed{\mathbf{110}}.

    4. Estimate the product: 23.8×34923.8 \times 349.

  10. Round each number to a suitable value for estimation.

    Round 23.8 to the nearest ten: 23.8≈2023.8 \approx 20.
    Round 349 to the nearest hundred: 349≈300349 \approx 300.

  11. Multiply the rounded numbers.

    20×300=600020 \times 300 = 6000

    The estimated product is 6000\boxed{\mathbf{6000}}.

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