How to do the 10

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The exponent (or index or power) of a number sayshow many times khổng lồ usethe number in a multiplication.

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102 means 10 × 10 = 100

(It says 10 is used 2 times in the multiplication)


Example: 103 = 10 × 10 × 10 = 1,000

In words: 103 could be called "10 khổng lồ the third power", "10 to the nguồn 3" or simply "10 cubed"

Example: 104 = 10 × 10 × 10 × 10 = 10,000

In words: 104 could be called "10 khổng lồ the fourth power", "10 khổng lồ the power 4" or "10 to the 4"

You can multiply any number by itself as many times as you want using this notation (see Exponents), but powers of 10 have a special use ...

Powers of 10

"Powers of 10" is a very useful way of writing down large or small numbers.

Instead of having lots of zeros, you show how many powers of 10 will make that many zeros


Example: 5,000 = 5 × 1,000 = 5 × 103

5 thousand is 5 times a thousand. & a thousand is 103. So 5 times 103 = 5,000

Can you see that 103 is a handy way of making 3 zeros?


Scientists and Engineers (who often use very big or very small numbers) lượt thích to write numbers this way.


Example: The Mass of the Sun

The Sun has a Mass of 1.988 × 1030 kg.

It is too hard khổng lồ write 1,988,000,000,000,000,000,000,000,000,000 kg

(And very easy khổng lồ make a mistake counting the zeros!)


Example: A Light Year (the distance light travels in one year)

It is easier to use 9.461 × 1015 meters, rather than 9,461,000,000,000,000 meters


It is commonly called Scientific Notation, or Standard Form.

Other Way of Writing It

Sometimes people use the ^ symbol (above the 6 on your keyboard), as it is easy to lớn type.


Example: 3 × 10^4 is the same as 3 × 104

3 × 10^4 = 3 × 10 × 10 × 10 × 10 = 30,000

*

Calculators often use "E" or "e" lượt thích this:


Example: 6E+5 is the same as 6 × 105

6E+5 = 6 × 10 × 10 × 10 × 10 × 10 = 600,000

Example: 3.12E4 is the same as 3.12 × 104

3.12E4 = 3.12 × 10 × 10 × 10 × 10 = 31,200

Example: What is 1.35 × 104 ?

You can calculate it as: 1.35 x (10 × 10 × 10 × 10) = 1.35 x 10,000 = 13,500

But it is easier to think "move the decimal point 4 places to lớn the right" like this:


1.3513.5135.

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1350.13500.

Negative Powers of 10

Negative? What could be the opposite of multiplying? Dividing!

A negative nguồn means how many times to divide by the number.


Just remember for negative powers of 10:

For negative powers of 10, move the decimal point to the left.

So Negatives just go the other way.


Example: What is 7.1 × 10-3 ?

Well, it is really 7.1 x (1/10 × 1/10 × 1/10) = 7.1 × 0.001 = 0.0071

But it is easier lớn think "move the decimal point 3 places to the left" lượt thích this:


7.10.710.0710.0071

Try It Yourself

Enter a number and see it in Scientific Notation:

Now try lớn use Scientific Notation yourself:

Summary


The index of 10 says how many places lớn move the decimal point. Positive means move it to lớn the right, negative means khổng lồ the left. Example: