A power of base ten is a number whose base is 10 raised to an integer power n. It results in the digit 1 followed by n zeros when the exponent is positive, or preceded by n zeros when the exponent is negative.
If the exponent n is negative:
In case the exponent is negative, we place a comma after the first zero.
Powers of base ten simplify writing and calculating with large numbers, with many orders or decimal places.
For example, the number 1 000 000 000 (one billion), can be written as (1 followed by nine zeros). Similarly, a number like 0.000 000 000 001 can be written as (1 preceded by twelve zeros).
It is worth remembering that this is due to the negative exponent inverting the fraction.
Multiplying and dividing powers of base 10
Multiplication and division of base-ten powers follow the same rules as for power.
When multiplying powers of ten, we repeat the base and add the exponents.
When dividing powers of base 10, we repeat the base and subtract the exponents.
Adding and subtracting powers of base 10
Addition and subtraction of powers of base ten can only occur if their exponents are equal. Thus, it is enough to treat the powers as integer values.
A power of ten squared plus a power of ten squared is equal to two powers of ten squared.
If the exponents are not equal, equalize them and only then add or subtract.
Changing the exponent in powers of base 10
To change the exponent without changing the value of the power, we multiply the power by 1 and move its decimal point as the exponent changes.
For increase the exponent, we move the decimal point in the digit 1 to the left, we add as many orders as units to the exponent.
Increase the power exponent by 3 without changing its value.
For decrease the exponent, we move the decimal point in the digit 1 to the right, as many orders as units we remove from the exponent.
Decrease the power exponent by 2 units , without changing its value.
(if we subtract two units in the exponent, we multiply by 100)
learn more at cientific notation and order of magnitude.
Exercises on powers of ten
Write the following numbers as powers of base 10.
Write the powers of base 10 as integers or decimals.
Perform operations with powers of base 10.
- Potentiation properties
- Strengthening Exercises
- Scientific notation exercises