Question

How do I write 780,000 in scientific notation.

I’m having finals and I need lots of help pls explain how u got it answer

Answer 1

780,000
`=7.8 * 10^5`

Explanation:

Don't worry! I hope you do great on your finals, goodluck<3.

What is scientific notation?

It's a way of expressing numbers that are either too large or too small.

The formula for scientific notation is written as shown below:

`a * 10^(b)`

Variable A represents a number thats absolute value has to be greater than or equal to 1 and less than 10. This is represented below

1 ≤ | a | < 10

Therefore we know that 780,000 will be 7.8, because it is greater than 1 and less than 10 as well can still represent our original number.

`7.8 * 10^b`

Assuming you know how powers work, if not I'll go over them very quickly.

What is an exponent?

An exponent(also called a power or indices) is a tells you how many time you are going to use the number in multiplying a number by itself.

For example 8² = 8 * 8, 8³ = 8 * 8 * 8.

To find what the exponent will be is pretty simple, you take 780,000 and identify what place our number is in.

what I mean by this is if its in, tenths, hundreths, thousands, 10 thousands..

It's pretty obvious that our number is in the 100 thousands place.

Now if you know you're powers pretty well, this will be easy, although let me try to walk you through it if not.

remember the equation:

`7.8 * 10^b`

We are trying to find b.

10 to what power is equal to 100,000

`10^(1) = 10, 10^(2) = 100, 10^3 = 100, 10^(3) = 1,000, 10^4 = 10,000, 10^5 = 100,000`

How I like to remember what a power equals is counting the 0's :)

How we know if our answer is correct is plugging it into our equation and solve:

`7.8 * 10^5`

We know that 10 to the power of 5 equals 100,000.

`7.8 * 100,000`

and using a calculator, or mental math, or doing it the old fashion way, we know that 7.8 * 100,000 is equal to 780,000

Answer 2

the scientific notation is just another mumble jumble way to write the same thing without so many repetitive zeros, so hmmm 780000 has 4 zeros, so what we do is we can say

78 and 4 zeros following it

or we can say

78 * 10⁴, if we get that product, is 780000

in scientific notation, we only leave one digit to the left of the decimal point

so the same thing above can be written as

78 * 10000, can be written as 78.0 * 10000

or as

7.8 * 100000

or as

0.78 * 1000000

check their product

7.8 * 100000, is really just 780000

because we moved the decimal to the left one more slot, it

became 7.8 * 100000

or in

scientific notation, 7.8 ⨉ 10⁵