Squaring numbers in the 900's
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- Choose a number in the 900s - start out easy with numbers near 1000; then go
lower when expert.
- Subtract the number from 1000 to get the difference.
- The first three places will be the number minus the difference: X X X _ _ _.
- The last three places will be the square of the difference: _ _ _ X X X
(if 4 digits, add the first digit as carry).
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Example:
- If the number to be squared is 985:
- Subtract 1000 - 985 = 15 (difference)
- Number - difference: 985 - 15 = 970: 9 7 0 _ _ _
- Square the difference: 15 × 15 = 225: _ _ _ 2 2 5
- So 985 × 985 = 970225.
See the pattern?
- If the number to be squared is 920:
- Subtract 1000 - 920 = 80 (difference)
- Number - difference: 920 - 80 = 840: 8 4 0 _ _ _
- Square the difference: 80 × 80 = 6400: _ _ _ 4 0 0
- Carry first digit when four digits: 8 4 6 _ _ _
- So 920 × 920 = 846400.
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