Powers of Ten
When multiplying like bases, keep the base and add exponents.
When finding the value of ten to a power, 10^{ n}, use 10
as a factor ‘n’ times. When dividing like bases, keep
the base and subtract exponents.
Example:
10^{ 2} x 10^{ 3} = 10^{ 2+3} = 10^{
5} = 10 x 10 x 10 x 10 x 10 = 100000.
10^{ 6} Ã· 10^{ 3} = 10^{ 63} = 10^{
3} = 10 x 10 x 10 = 1000
Multiplication and Division by powers of ten
A power of ten is a number that can be written as a product of
tens; 10, 100, 1000, 10,000 are powers of ten. In exponential
form, these are 10^{ 1}, 10^{ 2}, 10^{ 3},
and 10^{ 4}. A power of ten can be recognized by looking
for the number 10 written with an exponent or a single
‘1’ followed by zeros.
To multiply a number by a power of ten, move the decimal point
to the right.
To divide a number by a power of ten, move the decimal point
to the left. The number of places to move, either left or right,
is shown by the number of zeros in the power of ten. Zeros may
have to be placed to the right or the left of the number in order
to move the correct number of decimal places.
Examples
Multiply: 5.6(10,000)
10,000 has 4 zeros; therefore, 3 zeros have to be placed to
the right of the number, ‘5.6’, in order to move the
correct number of decimal places.
5.6(10,000) = 56,000
Divide: 5.6 Ã· 10,000
3 zeros have to be placed to the left of the number,
‘5.6’, in order to move the correct number of decimal
places.
5.6 Ã· 10,000 = .00056 3.828 x 100 = 382.8 382.8 Ã·1000 =
.3828
