Solution - Scientific notation/Standard form

3.234 \cdot 10^{- 3}

3.234*10^-3

See steps

Step-by-step explanation

1. Make the number a new number between 1 and 10

Move the decimal point to make 0.003234 a new number between 1 and 10. Because our original number is less than one, we move the decimal point to the right. Drop any zeroes in front of the number. Keep track of how many times we move the decimal point.

0.003234 -> 3.234

Our new number is 3.234. We moved the decimal point 3 times.

2. Define the power of 10

Because our original number was less than one, the exponent defining the power of 10 is negative. Remember, we moved the decimal point 3 times, so the exponent is negative 3

$10^{- 3}$

3. Final result

$3.234 \cdot 10^{- 3}$

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Why learn this

Scientific notation, or standard form, makes things easier when working with very small or very big numbers, both of which come up frequently in the fields of science and engineering. It is used in science, for example, to convey the mass of the heavenly bodies: Jupiter’s mass is $1.898 \cdot 10^{27}$ kg, which is easier to comprehend than writing the number 1,898 followed by 24 zeroes. Scientific notation also makes solving problems that use such high or low numbers more straightforward.

Terms and topics

Scientific notation