Multiplying by numbers ending in zeros

If the second factor ends in zeros, split off the significant part and a power of ten:

24 \cdot 300 = 24 \cdot 3 \cdot 100 = 72 \cdot 100 = 7200

First multiply the “short” numbers without the extra zeros, then append as many zeros as you set aside (or multiply by

10

100

1000

, and so on). The same works if the zeros are in the first factor:

180 \cdot 4 = 18 \cdot 10 \cdot 4 = 18 \cdot 4 \cdot 10

. You may swap the order of factors (

a\cdot b = b\cdot a

) when it helps.

Strip trailing zeros, multiply the short numbers, put the zeros back

\cdot 10

\cdot 100

, … — shifting places

Check: estimate the size (how many digits in the answer)

The times table for the nonzero digit — same as before

By 10 and by “round” tens

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