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Multiplying decimals

Multiplying decimals

Multiplying as whole numbers

3.25×2.4\displaystyle 3.25\times2.4: first multiply without the points, 325×24=7800\displaystyle {325\times24}={7800}. But 325\displaystyle 325 is 3.25\displaystyle 3.25 made 100 times bigger, and 24\displaystyle 24 is 2.4\displaystyle 2.4 made 10 times bigger – so 7800\displaystyle 7800 is 100×10=1000\displaystyle {100\times10}={1000} times too big. Make it 1000 times smaller: 3.25×2.4=7.800=7.8\displaystyle {3.25\times2.4}={7.800}={7.8}.

Checking with an estimate
An estimate catches a point in the wrong place.

Does it make sense? 3.25×2.4\displaystyle 3.25\times2.4 is close to 3×2.5=7.5\displaystyle {3\times2.5}={7.5} – so 7.8\displaystyle 7.8 is right, and 78\displaystyle 78 or 0.78\displaystyle 0.78 would not be.

Multiplying with fractions

Another way: decimals are fractions with 10, 100, 1000 … as the denominator. 0.25×0.3=25100×310=751000=0.075\displaystyle {0.25\times0.3}={\frac{25}{100}\times\frac{3}{10}}={\frac{75}{1000}}={0.075}.

The number of digits after the point

Multiply as whole numbers, and the result has as many digits after the point as both numbers together – 0.25\displaystyle 0.25 has two, 0.3\displaystyle 0.3 has one, 0.075\displaystyle 0.075 has three.

Exercise 1

Work it out as fractions, as in the example, and write the result as a decimal.

a

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

    b

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

      Exercise 2

      Estimate first, then calculate.

      a

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

        b

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

          c

            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

            d

              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

              Exercise 3

              Without calculating: which product is bigger, 9.1×0.33\displaystyle 9.1\times0.33 or 1×0.99\displaystyle 1\times0.99?
              Explain.