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Divide decimals by decimals

Division of positive decimals is understood as determining how many groups of a decimal size are contained in another quantity, or finding an unknown factor in a multiplication relationship. The quotient remains unchanged when both dividend and nonzero divisor are multiplied by the same power of ten, allowing place-value reasoning and the standard algorithm; estimates help detect misplaced decimal points. The scope includes finite decimals and reasonable approximations to hundredths, not more advanced algebraic or infinite-decimal treatments.

Detailed Explanation: Divide decimals by decimals

To divide by a decimal, make the divisor a whole number. Multiply both the dividend and divisor by the same power of 1010. This keeps the quotient unchanged.

Example: Find 3.75÷0.153.75 \div 0.15.

  1. Estimate first.
    Since 3.75≈43.75 \approx 4 and 0.15≈0.20.15 \approx 0.2, the answer should be around 4÷0.2=204 \div 0.2=20.

  2. Make the divisor a whole number.
    The divisor, 0.150.15, has two digits after the decimal point, so multiply both numbers by 100100:

3.75÷0.15=375÷15 3.75 \div 0.15 = 375 \div 15
  1. Divide.

    • 1515 goes into 3737 two times. Write 22.
    • 2×15=302\times 15=30, and 37−30=737-30=7.
    • Bring down the 55 to make 7575.
    • 1515 goes into 7575 five times. Write 55.

    Therefore,

375÷15=25 375\div 15=25

So,

3.75÷0.15=25\boxed{3.75\div 0.15=25}

The answer makes sense because 2525 is reasonably close to the estimate of 2020.

Learn by doing: Divide decimals by decimals

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Division as Fraction - Decimal x Decimal - Hundredths


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