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Round the number to the place of the underlined digit.

Mathematics

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Here are the solutions for rounding the numbers:

1. Round 49.012 to the place of the underlined digit.
The underlined digit is 0 in the tenths place.

  1. Identify the digit to the right of the tenths place, which is 1.

  2. Since 1<51 < 5, keep the tenths digit (0) as it is.

    49.012≈49.049.012 \approx \boxed{\text{49.0}}

    2. Round 2.308 to the place of the underlined digit.
    The underlined digit is 0 in the hundredths place.

  3. Identify the digit to the right of the hundredths place, which is 8.

  4. Since 8≥58 \ge 5, round up the hundredths digit (0) to 1.

    2.308≈2.312.308 \approx \boxed{\text{2.31}}

    3. Round 9.647 to the place of the underlined digit.
    The underlined digit is 4 in the hundredths place.

  5. Identify the digit to the right of the hundredths place, which is 7.

  6. Since 7≥57 \ge 5, round up the hundredths digit (4) to 5.

    9.647≈9.659.647 \approx \boxed{\text{9.65}}

    4. Round 7.519 to the place of the underlined digit.
    The underlined digit is 1 in the hundredths place.

  7. Identify the digit to the right of the hundredths place, which is 9.

  8. Since 9≥59 \ge 5, round up the hundredths digit (1) to 2.

    7.519≈7.527.519 \approx \boxed{\text{7.52}}

    5. Round 8.436 to the nearest hundredth.

  9. Identify the hundredths digit, which is 3.

  10. Identify the digit to its right, which is 6.

  11. Since 6≥56 \ge 5, round up the hundredths digit (3) to 4.

    8.436≈8.448.436 \approx \boxed{\text{8.44}}

    6. Round 15.159 to the nearest ten.

  12. Identify the tens digit, which is 1.

  13. Identify the digit to its right, which is 5.

  14. Since 5≥55 \ge 5, round up the tens digit (1) to 2.

    All digits to the right become 0.

    15.159≈2015.159 \approx \boxed{\text{20}}

    7. Round 1.602 to the nearest whole number.

  15. Identify the whole number (ones place) digit, which is 1.

  16. Identify the digit to its right, which is 6.

  17. Since 6≥56 \ge 5, round up the ones digit (1) to 2.

    1.602≈21.602 \approx \boxed{\text{2}}

    8. Round 3.619 to the nearest tenth.

  18. Identify the tenths digit, which is 6.

  19. Identify the digit to its right, which is 1.

  20. Since 1<51 < 5, keep the tenths digit (6) as it is.

    3.619≈3.63.619 \approx \boxed{\text{3.6}}

    9. Round 4.183.

    • Nearest whole number:
  21. The whole number digit is 4.

    The digit to its right is 1.

  22. Since 1<51 < 5, keep 4 as it is.

    $$
    \text{Nearest whole number: } \boxed{\text{4}}
    $$
    
    • Nearest tenth:
  23. The tenths digit is 1.

    The digit to its right is 8.

  24. Since 8≥58 \ge 5, round up 1 to 2.

    $$
    \text{Nearest tenth: } \boxed{\text{4.2}}
    $$
    
    • Nearest hundredth:
  25. The hundredths digit is 8.

    The digit to its right is 3.

  26. Since 3<53 < 5, keep 8 as it is.

    $$
    \text{Nearest hundredth: } \boxed{\text{4.18}}
    $$
    

    10. Round 9.076.

    • Nearest whole number:
  27. The whole number digit is 9.

    The digit to its right is 0.

  28. Since 0<50 < 5, keep 9 as it is.

    $$
    \text{Nearest whole number: } \boxed{\text{9}}
    $$
    
    • Nearest tenth:
  29. The tenths digit is 0.

    The digit to its right is 7.

  30. Since 7≥57 \ge 5, round up 0 to 1.

    $$
    \text{Nearest tenth: } \boxed{\text{9.1}}
    $$
    
    • Nearest hundredth:
  31. The hundredths digit is 7.

    The digit to its right is 6.

  32. Since 6≥56 \ge 5, round up 7 to 8.

    $$
    \text{Nearest hundredth: } \boxed{\text{9.08}}
    $$
    
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