Multiplying decimals by powers of ten means multiplying a decimal number by 10, 100, 1,000, or another power of ten. Each power of ten moves the digits to the left on the place value chart, changing the number’s value by that factor of ten.
Each zero in a power of ten moves the digits one place to the left, making the number ten times greater for every zero added.
A power of ten is a number like 10, 100, 1,000, and so on. We can also write powers of ten using exponents. For example, 101 = 10, 102 = 100, and 103 = 1,000.
Every time you increase the exponent by 1, the digits shift one place to the left. The value becomes ten times greater each time.
To multiply a decimal by a power of ten, move the decimal point to the right the same number of places as there are zeros in the power of ten, or as shown by the exponent.
Do not add or remove digits—just shift the decimal point to the right for multiplication by powers of ten.
When multiplying by powers of ten, each place value becomes ten times greater. Ones become tens, tenths become ones, and hundredths become tenths, and so on.
Each shift in place value represents multiplying by ten. Always track how far the digits move based on the number of zeros or the exponent.
To make sure your answer makes sense, estimate first. Multiplying by a power of ten should always make the number larger. If your product is smaller, recheck the decimal placement.
Always use estimation and place value reasoning to verify your work before moving to the next problem.