Our problem was 1.2 × 1.4, but we have calculated 12 × 14, so our work isn’t finished yet. We have
to place a decimal point in the answer. To find where we put the decimal, we look at the problem and
count the number of digits after the decimals in the multiplication. There are two digits after the
decimals: the 2 in 1.2 and the 4 in 1.4. Because there are two digits after the decimals in the problem,
there must be two digits after the decimal in the answer. We count two places from the right and put the
decimal between the 1 and the 6, leaving two digits after it.
1.68 Answer
An easy way to double-check this answer would be to approximate. That means, instead of using the
numbers we were given, 1.2 × 1.4, we round off to 1.0 and 1.5. This gives us 1.0 times 1.5, which is 1.5,
so we know the answer should be somewhere between 1 and 2. This tells us our decimal is in the right
place. This is a good double-check. You should always make this check when you are multiplying or
dividing using decimals. The check is simply: does the answer make sense?
Let’s try another.
9.6 × 97 =
We write the problem down as it is, but work it out as if the numbers are 96 and 97.
96 − 3 = 93
93 × 100 (reference number) = 9,300
4 × 3 = 12
9,300 + 12 = 9,312
Where do we put the decimal? How many digits follow the decimal in the problem? One. That’s how
many digits should follow the decimal in the answer.
931.2 Answer
To place the decimal, we count the total number of digits following the decimals in both numbers we
are multiplying. We will have the same number of digits following the decimal in the answer.
We can double-check the answer by estimating 10 times 90; from this we know the answer is going to
be somewhere near 900, not 9,000 or 90.
If the problem had been 9.6 × 9.7, then the answer would have been 93.12. Knowing this can enable
us to take some shortcuts that might not be apparent otherwise. We will look at some of these
possibilities shortly. In the meantime, try these problems.
Test yourself
Try these:
a) 1.2 × 1.2 =
b) 1.4 × 1.4 =
c) 12 × 0.14 =
d) 96 × 0.97 =
e) 0.96 × 9.6 =
f) 5 × 1.5 =