Understanding Powers of Ten

A power of ten is simply the number 10 multiplied by itself a certain number of times. We use exponents to write this in a short, easy way.

What are Powers of Ten?

In a power of ten, the small raised number is called the exponent. It tells you how many times to multiply 10 by itself. A quick trick: the exponent also tells you exactly how many zeros come after the 1!

• $10^1 = 10$ (One zero)
• $10^2 = 10 \times 10 = 100$ (Two zeros)
• $10^3 = 10 \times 10 \times 10 = 1{,}000$ (Three zeros)
• $10^4 = 10 \times 10 \times 10 \times 10 = 10{,}000$ (Four zeros)

Multiplying by Powers of Ten

When you multiply a number by a power of ten, the number gets larger. To find the answer, simply shift the decimal point to the right by the number of places matching the exponent (or the number of zeros). If you run out of digits, add zeros as placeholders.

Example: Calculate $3.45 \times 10^3$

• The exponent is $3$, so we move the decimal point $3$ places to the right.
• $3.45 \rightarrow 34.5 \rightarrow 345. \rightarrow 3{,}450$
• Answer: $3{,}450$

Dividing by Powers of Ten

When you divide a number by a power of ten, the number gets smaller. You find the answer by shifting the decimal point to the left by the number of places matching the exponent.

Example: Calculate $678 \div 10^2$

• The exponent is $2$, so we move the decimal point $2$ places to the left. (Remember, a whole number like $678$ has an invisible decimal at the end: $678.0$).
• $678.0 \rightarrow 67.8 \rightarrow 6.78$
• Answer: $6.78$

Practice Examples

1. Calculate $3.45 \times 10^3$ Move the decimal $3$ places right: $3.45 \times 1{,}000 = 3{,}450$.

2. Calculate $678 \div 10^2$ Move the decimal $2$ places left: $678 \div 100 = 6.78$.

3. Write $10{,}000$ as a power of $10$ Count the zeros. There are $4$ zeros, so the exponent is $4$. The answer is $10^4$.