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Use tables of reciprocals to find the reciprocal of 0.3758. Hence find the value [3]0.1250.3758 correct to 4.S.f

Mathematics

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Answer

1.331

Step-by-step solution

4 steps

Huu hapa ni ufumbuzi wa swali la 14:

  1. Pata reciprocal ya 0.3758.

    Reciprocal ya namba xx ni 1x\frac{1}{x}.
    Kwa kuwa hatuna jedwali la reciprocals, tutatumia hesabu ya moja kwa moja (ambayo ingetoa thamani sawa na jedwali):

    10.3758≈2.661000532\frac{1}{0.3758} \approx 2.661000532

    Kuzungusha hadi tarakimu 4 muhimu (4 s.f.):

    Reciprocal ya 0.3758≈2.661\text{Reciprocal ya } 0.3758 \approx 2.661
  2. Pata thamani ya 0.1253\sqrt[3]{0.125}.

    0.1253=12510003=183=1383=12=0.5\sqrt[3]{0.125} = \sqrt[3]{\frac{125}{1000}} = \sqrt[3]{\frac{1}{8}} = \frac{\sqrt[3]{1}}{\sqrt[3]{8}} = \frac{1}{2} = 0.5
  3. Tafuta thamani ya 0.12530.3758\frac{\sqrt[3]{0.125}}{0.3758}.

    Sasa tunaweza kubadilisha thamani tulizopata kwenye usemi:

    0.12530.3758=0.50.3758\frac{\sqrt[3]{0.125}}{0.3758} = \frac{0.5}{0.3758}

    Hii pia inaweza kuandikwa kama 0.5×(10.3758)0.5 \times \left(\frac{1}{0.3758}\right).
    Kutumia thamani kamili zaidi ya reciprocal kutoka Hatua ya 1:

    0.5×2.661000532≈1.3305002660.5 \times 2.661000532 \approx 1.330500266
  4. Zungusha jibu hadi tarakimu 4 muhimu (4 s.f.).

    Tarakimu 4 za kwanza za 1.330500266 ni 1,3,3,01, 3, 3, 0. Tarakimu ya tano ni 5, kwa hivyo tunazungusha tarakimu ya nne (0) kwenda juu.

    1.330500266≈1.3311.330500266 \approx 1.331

    Kwa hiyo,
    Reciprocal ya 0.3758 ni 2.661\mathbf{2.661} (kwa 4 s.f.).
    Na thamani ya usemi ni:

    1.3311.331
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