Powers of Base Ten

What Do Billions and Billionths Mean?

Working with powers of 10 is simply a matter of moving the decimal point.
Working with powers of 10 is simply a matter of moving the decimal point. Caspar Benson, Getty Images

What do you call different powers of ten and what are their values? It can be confusing when you read about billions, and then suddenly shift to billionths. Let's take a look at the values and names of the powers of ten.

What Does a Power Mean? Exponents and Scientific Notation

Raising a number to a power means that you multiply it by itself. The number itself would be that number to the power of one.

When you multiply it by itself, it is now that number to the power of two. The power is designated as an exponent with a small superscript number following the number itself.

Ten is an easy number to visualize with powers, as you can think of the exponent number as being the number of zeros to put behind the one. Ten to the zero power is 10 divided by 10, or 1 with no zeroes behind it, which equals one. Ten to the second power is a 1 followed by two zeroes, or 100.

When you divide a number by itself more than once, the power (or exponent) value is negative. A -1 power means you have divided a number by itself twice (10/10/10) and a  -2 power means you have divided a number by itself three times (10/10/10/10) . In the case of 10, since 10 to the zero power is one, it is easier to think of one being divided 10 in the increments shown in the exponent.

Powers of Ten

Trillions

1012 = 1,000,000,000,000
10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000,000,000

Billions

109 = 1,000,000,000
10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000,000

Millions

106= 1,000,000
10 x 10 x 10 x 10 x 10 x 10 = 1,000,000

Hundred Thousands

105 = 100,000
10 x 10 x 10 x 10 x 10 = 100,000

Ten Thousands

104 = 10,000
10 x 10 x 10 x 10 = 10,000

Thousands

103 = 1,000
10 x 10 x 10 = 1,000

Hundreds

102 = 100
10 x 10 = 100

Tens

101 = 10
ones
100 = 1

Tenths

10-1 = 1/1 1 = 1/10
1/10 = 0.1

Hundredths

10-2 = 1/102 = 1/100
1/10/10 = 0.01

Thousandths

10-3 = 1/10 = 1/1000
1 / 10 / 10 / 10 = 0.001

Ten Thousandths

10-4 = 1/104 = 1/10,000
1 / 10 / 10 / 10 / 10 = 0.0001

Hundred Thousandths

10-5 = 1/105 = 1/100,000
1 /10 /10 / 10 / 10 / 10 = 0.00001

Millionths

10-6 = 1/106 = 1/1,000,000
1 / 10 / 10 / 10 / 10 / 10 / 10 = 0.000001

Billionths

10-9 = 1/109 = 1/1,000,000,000
1 / 10 / 10 / 10 / 10 / 10 / 10 / 10 / 10 / 10 = 0.000000001

Trillionths

10-12 = 1/1012 = 1/1,000,000,000,000
1 / 10 / 10 / 10 / 10 / 10 / 10 / 10 / 10 / 10 / 10 / 10 / 10 = 0.000000001

See more names of numbers that are powers of ten, including the octillion, googol, and googolplex.

Lessons with Powers of Ten

Powers of Ten Multiplication Worksheets:  See worksheets you can use to practice multiplying two- and three-digit numbers by different powers of ten. These seven worksheet variations can be used to practice multiplication. Each sheet has 20 numbers and asks you to multiply them by 10, 100, 1000, 10,000 or 100,000. 

Multiplication Worksheets with Powers of Tens to the Hundredths Place: Practice decimal multiplication with these worksheets. Working out the answers without using a calculator can enhance understanding of the process and the effects of dividing with small numbers.

Edited by Anne Marie Helmenstine, Ph.D.