How to use scientific notation

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PSAT Math › How to use scientific notation

Questions 1 - 4

Express the square of $7 \times 10^{15}$ in scientific notation.

$4.9 \times 10^{31}$

$49 \times 10^{30}$

$4.9 \times 10^{226}$

$49 \times 10^{225}$

$4.9 \times 10^{16}$

Explanation

Take advantage of the exponent rules.

$\left (7 \times 10^{15} \right )^{2}$

$= 7^{2} \times \left ( 10^{15} \right )^{2}$

$= 49 \times 10^{15 \times 2}$

$= 49 \times 10^{30}$

$= 4.9 \times 10^{1} \times 10^{30}$

$= 4.9 \times 10^{1+30}$

$= 4.9 \times 10^{31}$

The number is equivalent to which of the following?

$2.79\cdot 10^{-5}$

$2.79\cdot 10^{-4}$

$2.79\cdot 10^{4}$

$2.79\cdot 10^{5}$

$2.79\cdot 10^{-6}$

Explanation

Each of the answers to this question are in scientific notation. To determine the exponent on the 10, see how many places you need to move the decimal over to get from your original number to 2.79.

Scientific_notation

Because the decimal place moves 5 places, the exponent will be 5, and because the decimal moves to the RIGHT, the exponent is going to be negative.

So the answer to the quesiton is $2.79\cdot 10^{-5}$

Put the following value in scientific notation:

$1.954 \times 10^{7}$

$1.954 \times 10^{6}$

$19.54 \times 10^{7}$

$1954 \times 10^{4}$

Explanation

Our first value for scientific notation should be between and . We then multiply this value by raised to a power equal to the number of spaces our decimal has moved to the left.

Express 0.000000076 in scientific notation.

$7.6 \times 10^{-8}$

$7.6 \times 10^{-9}$

$7 6 \times 10^{-8}$

$7 6 \times 10^{-9}$

$0.76\times 10^{-8}$

Explanation

Write the number:

Counting the number of places, move the decimal point to the right until it is after the first nonzero digit:

The resulting number is 7.6; the number of places the decimal point moved to the right was 8. In scientific notation, this number is $7.6 \times 10^{-8}$ .

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