To multiply two decimals, first ignore the decimal points and multiply
the numbers as if they were whole numbers. Then count how many decimal places the two
original numbers had together, and put that many decimal places back into the
answer.
For example, to work out 0.3 \times 0.4: ignore the points and
multiply 3 \times 4 = 12. The two numbers had one decimal place
each — two in total — so the answer has two decimal places:
0.3 \times 0.4 = 0.12
Multiplying or dividing by 10, 100
or 1000 is even simpler: it just shifts the digits
past the point. Multiplying by 10 moves the point one place to
the right; dividing by 10 moves it one place to
the left:
2.5 \times 10 = 25 \qquad 2.5 \div 10 = 0.25
Each extra zero in the power of ten shifts the point one more place
(\times 100 two places right, \div 1000
three places left).
To divide by a decimal, first turn the divisor into a whole number. You do
this by multiplying both numbers by 10,
100 or whatever it takes — scaling both up by the same amount
keeps the answer the same.
For example, 2.4 \div 0.6: multiply both numbers by
10 so the divisor 0.6 becomes the
whole number 6. Now it is an easy whole-number division:
2.4 \div 0.6 = 24 \div 6 = 4
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To multiply: ignore the points, multiply as whole numbers, then put
back as many decimal places as the two numbers had together.
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To multiply or divide by a power of ten: shift the point right
(multiply) or left (divide) — one place per zero.
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To divide by a decimal: scale both numbers up by the same power of ten
so the divisor becomes a whole number, then divide.