Scientific notation

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You can use scientific notation to write very large or very small numbers. Here are some examples.

4,000,000 in scientific notation is

0.00007 in scientific notation is

–

Writing numbers in scientific notation can make them easier to work with.

How do you read numbers in scientific notation?

You can interpret scientific notation by converting the number to standard form. Just follow the rules for multiplying by a

power of

When you multiply by a power of 10, the exponent in the power of 10 tells you how many places to move the decimal point. Follow these rules:

If the exponent is positive, move the decimal point to the
right.
If the exponent is negative, move the decimal point to the
left.

Let's try it! The planet Neptune is about

2.78

miles from the sun. Write

2.78

in standard form.

The exponent in

is positive 9, so move the decimal point 9 places to the right.

So,

2.78

in standard form is 2,780,000,000.

Another example

The average grain of sand weighs about

4.4

–

kilograms. Write

4.4

–

in standard form.

The exponent in

–

is negative 6, so move the decimal point 6 places to the left.

So,

4.4

–

in standard form is 0.0000044.

How do you write numbers in scientific notation?

You can write numbers in scientific notation by writing them as a product of two factors.

The first factor is always a number greater than or equal to 1 but less than 10.
The second factor is always a power of 10.

For example, you can write the number 561,000,000 in scientific notation as

5.61

To determine the two factors, follow these steps:

Move the decimal point in the number until you get a number greater than or equal to 1 but less than 10. This will be the first factor.
Count how many places, and in which direction, you moved the decimal point. This will tell you the exponent in the power of 10. If you moved the decimal point to the left, your exponent will be positive. If you moved the decimal point to the right, your exponent will be negative.

Let's try it! Write 0.000095 in scientific notation.

Start by writing the first factor. Move the decimal point between 9 and 5. The first factor is 9.5.

Then, determine the exponent in the power of 10. Count the number of places the decimal point moved to make 9.5. Since you'll need to move the decimal to the right, use a negative exponent.

The decimal point moved 5 places to the right, so the second factor is

–

So, the number 0.000095 in scientific notation is

9.5

–

Try some practice problems!

Convert between standard and scientific notation

Scientific notation on calculators

Different calculators will show numbers in scientific notation in different ways.

For example, the number 450,000,000 may be displayed in the following ways:

You can also input a number in scientific notation on a calculator. Look for a key with EE or EXP on it. This key tells the calculator to multiply by a power of 10.

For example, to input the number

1.34

on a calculator, start by inputting the first factor, 1.34. Then, press the EE or EXP key. Last, input the exponent on the power of 10, 7.

Try some practice problems!

Scientific notation on calculators

Compare numbers written in scientific notation

You can compare two numbers written in scientific notation by following these steps:

Compare the powers of 10. If one of the powers of 10 is greater than the other, that number is greater.
If the powers of 10 are the same, compare the first factors. If one of the first factors is greater than the other, that number is greater.

Let's try it! Compare

4.7

and

3.6

Start by comparing the powers of 10. Since

then

4.7

3.6

You can see why this works by rewriting each number in standard form.

4.7

= 470,000,000

3.6

= 3,600,000,000

Since

470,000,000

3,600,000,000

then

4.7

3.6

Another example

Compare

5.1

–

and

2.8

–

Start by comparing the powers of 10. Since they are the same, compare the first factors.

Compare the first factor in each number. Since

5.1

2.8

then

5.1

–

2.8

–

You can see why this works by rewriting each number in standard form.

5.1

–

= 0.00000051

2.8

–

= 0.00000028

Since

0.00000051

0.00000028

then

5.1

–

2.8

–

Try some practice problems!

Compare numbers written in scientific notation

Skills

Convert between standard and scientific notation Scientific notation on calculators Compare numbers written in scientific notation

Videos(3)

Convert between standard and scientific notation

Scientific notation on calculators

Compare numbers written in scientific notation

Lessons

Powers of 10

Adding and subtracting numbers in scientific notation

Multiplying and dividing numbers in scientific notation

How do you read numbers in scientific notation?

Another example

How do you write numbers in scientific notation?

Try some practice problems!

Scientific notation on calculators

Try some practice problems!

Compare numbers written in scientific notation

Another example

Try some practice problems!

Related

Skills

Videos(3)

Lessons