Multiplying or Dividing by a Power of Ten 3-7
We have learned that in a decimal or a whole number each place value is ten times the place value to its right.
10 ∙ 1 = 10 10 ∙ 10 = 100 10 ∙ 100 = 1000
10 ∙ 0.1 = 1 10 ∙ 0.01 = 0.1 10 ∙ 0.001 = 0.01
Notice that multiplying by ten has resulted in the decimal point being moved one place to the right and in zeros being inserted or dropped.
Multiplying by ten moves the decimal point one place to the right
10 ∙ 762 = 7620 = 7620
10 ∙ 4.931 = 49.31
At the beginning of this chapter you learned about powers of ten
104 = 10 ∙10 ∙ 10 ∙10 = 10,000
We can see that multiplying by a power of 10 is the same as multiplying by 10 repeatedly.
2.64874 ∙104 = 2.63874 = 26,387.4
Notice that we have moved the decimal point four places to the right.
Rule
To multiply a number by the nth power of ten, move the decimal point n places to the right.
Powers of ten provide a convenient way to write very large numbers. Numbers that are expressed as products of a number greater than or equal to 1, but less than 10, AND a power of ten are said to be written in scientific notation.
To write a number in scientific notation we move the decimal point to the left until the resulting number is between 1 and 10. We then multiply this number by the power of 10, whose exponent is equal to the umber of places we moved the decimal point.
4,592,000,000 in scientific notation
First move the decimal point to the left to get a number between 1 and 10
4,592,000,000 4.592
Since the decimal point was moved 9 places, we multiply 4.592 by 109 to express the number in scientific notation
4.592 x 109
When we move a decimal point to the left, we are actually dividing by a power of ten.
Notice that in dividing by a power of 10 we move the decimal point to the left the same number of places as the exponent. Sometimes we may have to add zeros
3.1 ÷ 104 = 0003.1 = 0.00031
Rule
To divide a number by the nth power of ten, move the decimal point n places to the left, adding zeros as necessary.
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