Question

The size of a cell is typically found by capturing an image under a microscope then using software to measure its diameter. Two cells are measured using this method: Cell E: 8.39 x 10-² centimeters Cell F: 6.01 x 10-3 centimeters What's the difference between the diameters of the two cells? Express your answer using either standard notation or scientific notation.​

Answer 1

7.789×10^-2 = 0.07789 cm

Explanation:

Your calculator can find the difference of the two given diameters and express it in any format you like.

The attached image of a calculator display shows the difference of the cell diameters is 0.07789 = 7.789×10^-2 cm.

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The difference of two numbers with different exponents is found by first adjusting the exponents so they are the same. Here, we choose to adjust both numbers so they have the highest exponent value.

8.83×10^-2 - 6.01×10^-3

= 8.39×10^-2 - 0.601×10^-2 = (8.39 -0.601)×10^-2 = 7.789×10^-2

Alternatively, you can convert both numbers to standard form and do the subtraction that way.

8.83×10^-2 - 6.01×10^-3

= 0.0883 -0.00601 = 0.07789

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Additional comment

The second attachment shows the relationship between place values and their multiplier in scientific notation.

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The choice of exponent when computing the sum or difference of numbers in scientific notation is usefully informed by an estimate of the value of the sum or difference. A proper choice can avoid the need to adjust the exponent of the result of the operation. Here, we see the subtraction will change the larger value by less than 10%, so the exponent of the result in scientific notation will be that of the larger value (-2).