# How do you write 35, 615 in scientific notation?

May 10, 2018

The number in question is written $3.5615 \times {10}^{4}$ in SN

#### Explanation:

Converting values to SN or Scientific Notation means first writing the number as if it was less than 10, and then figuring out what multiple of 10 it needs to be multiplied by to get the original value.

If we write the original number as a value less than 10:

$35 , 615 \rightarrow 3.5615$

Now, to figure out the value it needs to be multiplied, we can simply divide the original number by the reduced value:

$\frac{35 , 615}{3.5615} = 10 , 000$

Finally, we figure out what the multiple needs to be written as, when given as an exponent of 10. The way to do this is to count the number of zeroes, starting at the ones place.

For the number 10,000, there are 4 zeroes, starting at the ones place. This means:

$10000 = {10}^{4}$

Now, we can finish the conversion:

$35615 = 3.5615 \times {10}^{4}$

May 10, 2018

$\implies 3.5615 \times {10}^{4}$

#### Explanation:

We rewrite the number where the most significant digit is on the left of the decimal and the rest of the trailing digits are on the right of the decimal:

$3.5615$

The number of decimal places we moved (in this case $4$ to the left) determines the power of $10$ to multiply by. Moving to the left is a positive power, moving to the right is negative power. So here we have a positive power of $4$.

$35615 \to 3.5615 \times {10}^{4}$