### 5.1.5 Scientific Notation

This subsection is not completed yet, but in the meantime here are some practice questions.

Remember:
To convert a number in scientific notation to decimal notation, the exponent tells you how many jumps the decimal point should make, e.g. $9.1273 \times 10^3 = 9127.3$ because the decimal point moves $3$ places.

Add zeros if necessary, e.g. $1.7 \times 10^4 = 17000$.

If the exponent is negative then the decimal point moves to the left, e.g. $3.42 \times 10^{-3} = 0.00342$ because the decimal point moves $3$ places to the left, and we put zeros in the empty places. A quick way to work it out is that the number of zeros you need to add is given in the exponent ($10^{-3}$ means $3$ zeros should be added).

Remember:
To write something in scientific notation, shift the decimal point until it’s after the first significant figure. If the decimal point needs to move to the left then the exponent is the number of jumps made by the decimal point, e.g. $158.29 = 1.5829 \times 10^2$ because we had to move the decimal point $2$ places to the left.

If you need to write a whole number in scientific notation, then consider the decimal point to start after the number, e.g. $38527 = 38527. = 3.8527 \times 10^4$ because we had to move the decimal point $4$ places to the left.

Zeros at the end of a whole number are most likely not significant, so they can be removed after converting, e.g. $15000 = 1.5\times10^4$.

If the decimal point needs to move to the right, then the exponent will be negative, e.g. $0.00386 = 3.86 \times 10^{-3}$ because we had to move the decimal point $3$ places to the right. A quick way to work it out is that the number of zeros at the front tells you the exponent: $3$ zeros means the exponent is $-3$.