Solution - Scientific notation/Standard form

7.5150225 \cdot 10^{7}

7.5150225*10^7

See steps

Step-by-step explanation

1. Write the number as a decimal

75150225.0

2. Make it a new number between 1 and 10

Move the decimal point to make 75150225.0 a new number between 1 and 10. Because our number is greater than 10, we move the decimal point to the left. Drop any trailing zeros and place the decimal point after the first non-zero digit. Keep track of how many times we move the decimal point.

75150225.0 -> 7.5150225

Our new number is 7.5150225. We moved the decimal point 7 times.

3. Define the power of 10

Because our original number was greater than 10, the power of 10 is positive. Remember, we moved the decimal point 7 times, so the exponent is positive 7:

$10^{7}$

4. Final result

$7.5150225 \cdot 10^{7}$

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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