Scientific Notation

## Scientific Notation

## The number 123 can be written as 100 + 20 + 3 or as (1 x 10^{2}) + (2 x 10^{1}) + (3 x 1). The digit 1 stands for 1 times 100; the digit 2 stands for 2 times 10; and the digit 3 stands for 3 times 1.

## We say these digits have the following *place values*:

- 1 is in the hundreds place.
- 2 is in the tens place.
- 3 is in the units (ones) place.

Every digit in a decimal number has a place value. The next places to the left of 123 are the thousands place, the ten-thousands place, the hundred-thousands place, the millions place, and so on. Digits to the right of the decimal point also have place values. For example 0.56 = 0.5 + 0.06 = (5 x 10^{-1}) + (6 x 10^{-2}); the digit 5 is in the tenths place, and the digit 6 is in the hundredths place.

Sometimes, using the concept of place value can let you write a very big or small number in a much shorter form. For example:

- 2,300,000,000,000 = 2.3 x 10
^{12} - 0.0000000007 = 7 x 10
^{-10}

Because such numbers often occur in scientific calculations, writing a number as the product of a power of 10 and a number greater than or equal to 1 and less than 10 is called *scientific notation*.

**Try it yourself**

1.) In 2000, there were approximately 281,000,000 people in the United States. Express this number in scientific notation.

2.) In the United States, 15,000,000 households use private wells for their water supply. Write this number in scientific notation.

3.) The United States has a total of 1.2916 x 10^{7} acres of land reserved for state parks. Write this number in standard form.

4.) Write the number in scientific notation:

0.00000000342

5.) Write the numbers in standard form:

a) 6.35 x 10

^{-6}

b) 2.83 x 10

^{12}

6.) About how many times larger is 9.0 x 10^{8} than 4.0 x 10^{6}?

**Answer key**

1.) 2.81 x 10^{8}

2.) 1.5 x 10^{7}

3.) 12,916,000

4.) 3.42 x 10^{-9}

5.) a) 0.00000635; b) 2,830,000,000,000

6.) 225