Which of the following expressions is correctly written in scientific notation?

a.1.4 × 10 5
b.0.32 × 10 3
c.5.62 × 2 10
d.11.2 × 10 1

The Answer is A. 1.4 x 10^5

Step-by-step explanation:

Numbers in Scientific notation have the first number between 1 and 9 and then the decimal, followed by the rest of the numbers. Find the power of 10 by moving the decimal one place a time from right to left until the decimal is between the last number and the next to last.

B. is wrong because the number is .32 x 10^3 instead of 3.2 x 10^2

C. is wrong because it is 2 to the 10th power (2^10) instead of a power of 10

D is wrong because the number is 11.2 x 10^1 instead of 1.12 x 10^2

Hope this helps :-)

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

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x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

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x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!