Pls explain how u divide that 1/0.1+1/0.2+1/0.3 i dont understand pls

Mathematics

ScanSolve AI Answer

Answer

18.333...\text{18.333...}

Step-by-step solution

4 steps

No problem, CØTBØJ. Let's break down that calculation step by step.

The expression was:

10.1+10.2+10.3\frac{1}{0.1} + \frac{1}{0.2} + \frac{1}{0.3}
  1. Calculate the first term, 10.1\frac{1}{0.1}.

    To divide by a decimal, you can convert the decimal to a fraction or multiply the numerator and denominator by a power of 10 to make the denominator a whole number.

    10.1=1110=1×101=10\frac{1}{0.1} = \frac{1}{\frac{1}{10}} = 1 \times \frac{10}{1} = 10

    Alternatively, multiply numerator and denominator by 10:

    1×100.1×10=101=10\frac{1 \times 10}{0.1 \times 10} = \frac{10}{1} = 10
  2. Calculate the second term, 10.2\frac{1}{0.2}.

    10.2=1210=1×102=5\frac{1}{0.2} = \frac{1}{\frac{2}{10}} = 1 \times \frac{10}{2} = 5

    Alternatively, multiply numerator and denominator by 10:

    1×100.2×10=102=5\frac{1 \times 10}{0.2 \times 10} = \frac{10}{2} = 5
  3. Calculate the third term, 10.3\frac{1}{0.3}.

    10.3=1310=1×103=3.333...\frac{1}{0.3} = \frac{1}{\frac{3}{10}} = 1 \times \frac{10}{3} = 3.333...

    Alternatively, multiply numerator and denominator by 10:

    1×100.3×10=103≈3.3333\frac{1 \times 10}{0.3 \times 10} = \frac{10}{3} \approx 3.3333
  4. Add the results from Step 1, Step 2, and Step 3.

    10+5+3.333...=18.333...10 + 5 + 3.333... = 18.333...

    So, the sum is 18.333...\text{18.333...}.

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