2000 x 100 = 200000
2000 times 100 is 200000. Both numbers are a single digit followed by zeros, so the whole job is counting zeros rather than multiplying. Here is the method and the mistake it prevents.
2,000 × 100 = 200,000
Adding 2,000 to itself 100 times gives the same answer.
Count the zeros
Strip the zeros off both numbers first. That leaves 2 x 1 = 2. Now count what you removed: three zeros from 2000, two from 100, five in total. Write the 2 and put five zeros behind it, giving 200000. Read aloud, two hundred thousand.
Why other pairs give the same answer
Only the total number of zeros matters, so moving a zero from one factor to the other leaves the product alone. Each of these is five zeros behind a 2:
- 2000 x 100
- 200 x 1000
- 10000 x 20
- 20000 x 10
All four come to 200000. If you are checking someone else’s working, that is a fast way to confirm it without repeating the multiplication.
Where this goes wrong
The error is always one zero, in one direction or the other. 2000 x 1000 is 2000000, ten times bigger, and 2000 x 10 is 20000, ten times smaller. Nothing else in this calculation can fail, so count the zeros twice and write it down once.
The size of 200000
200000 is a 2 followed by five zeros. At 2000 a month it is 100 months of income, a little over eight years. Its only prime factors are 2 and 5, which is true of every number made of a single digit and a run of zeros. More pairs on the multiplication answers page.