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MULTIPLYING BY POWERS OF TEN
Jump right to the exercises!
The concepts for this exercise are summarized below.
For a complete discussion, read the text.
In the base ten number system, it is extremely easy to
multiply by powers of ten.
To multiply by 101 = 10 , put 1 zero at the end of the number:
237 · 10 = 2,370 .
To multiply by 102 = 100 , put 2 zeros at the end of the number:
237 · 100 = 23,700 .
To multiply by 10n (which is 1 followed by n zeroes),
put n zeros at the end of the number.
For example, 237 · 107 = 2,370,000,000 .
Think about why this is so easy!
When, say, 237 is multiplied by 10 , the 2 hundreds
become 2 thousands; the 3 tens become 3 hundreds; and the 7 ones become 7 tens.
Each digit needs to shift into the next-left place value. Putting the zero at the end of the
number accomplishes this.
Here, you will practice multiplying by powers of ten.
Do NOT insert commas in your answers for this web exercise.
That is, type the answer to 631×103 as 631000 , NOT 631,000 .