Use the equation 135•42=5,670 and what you know about fractions, decimals, and place value to explain how to place the decimal point when you compute (1.35)•(4.2).

1.35 = 135/100

4.2 = 42/10

so the product of these fractions is ...

  (135/100)·(42/10) = (135·42)/(100·10) = 5670/1000 = 5.670

That is, ...

  1.35 · 4.2 = 5.670

As you know, the 5 in 1.35 is in the hundredths place. So the number 1.35 is 135 hundredths, or 135/100. The number of zeros in the denominator of this fraction is the number of decimal places in the number 1.35.

The 2 in the number 4.2 is in the tenths place. So the number 4.2 is 42 tenths, or 42/10. The number of zeros in the denominator of this fraction is the number of decimal places in the number 4.2.

When the fractions are multiplied, the numerator is the product of the integer numerators of the fractions. The denominator is the product of the denominators of the fractions. The denominator product will have a number of zeros that is the sum of the numbers of zeros in the denominators being multiplied. That is, 100 · 10 = 1000. The first number has 2 zeros; the second number has 1 zero; and the product has 2+1=3 zeros.

The product fraction 5670/1000 is telling you that the least significant digit of the numerator goes in the thousandths place of the corresponding decimal number, 5.760. That is, the number of decimal places in the answer is the sum of the number of decimal places in the numbers being multiplied.

It is important to keep the trailing zeros in this multiplication process. After you place the decimal point in the answer, then you can drop the trailing zeros if necessary or desirable.

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