Q: Given $$8.17 \times 10^8$ + 1.25 \times 10^9$, what is the correct first step to add these numbers?

Rewrite $$1.25 \times 10^9$ as 12.5$$ \times $$10^8.$$

Q: If you need to add $$2.5 \times 10^3$ and 3.0$$ \times $$10^2$$, what should you do first?

Rewrite $$3.0 \times 10^2$ as 0.30$$ \times $$10^3$$

Question 1

When adding or subtracting numbers in scientific notation, which of the following must be true before performing the operation?

Accepted Answer

The exponents must be the same.

Question 2

Given $$8.17 	imes 10^8$ + 1.25 	imes 10^9$, what is the correct first step to add these numbers?

Accepted Answer

Rewrite $$1.25 	imes 10^9$ as 12.5$$ 	imes $$10^8.$$

Question 3

Calculate $$8.17 	imes 10^8$ + 1.25 	imes 10^9$ and express your answer in scientific notation with the correct number of decimal places.

Accepted Answer

$$2.07 	imes 10^9$

Question 4

When adding or subtracting values in scientific notation, the final answer should have:

Accepted Answer

The least number of decimal places as the original numbers.

Question 5

Which of the following is the correct result for $$9.08 	imes 10$$^{-11}$$ - 1.17 	imes 10$$^{-12}$$ - 3.35 	imes 10$$^{-13}$$?

Accepted Answer

$$8.93 	imes 10$$^{-11}$$

Question 6

If you need to add $$2.5 	imes 10^3$ and 3.0$$ 	imes $$10^2$$, what should you do first?

Accepted Answer

Rewrite $$3.0 	imes 10^2$ as 0.30$$ 	imes $$10^3$$

Question 7

A laboratory result is reported as $$4.7 	imes 10^5$ cells/mL. If another sample has 3.2$$ 	imes $$10^4$$ cells/mL, what is the total cell count when the two samples are combined?

Accepted Answer

$$5.02 	imes 10^5$ cells/mL

Question 8

Which of the following best explains why exponents must be the same when adding or subtracting numbers in scientific notation?

Accepted Answer

So that the coefficients represent the same magnitude and can be directly added or subtracted.

Question 9

A student adds $$5.6 	imes 10^7$ and 2.4$$ 	imes $$10^8$$ and gets $$8.0 	imes 10^8$. What mistake did the student most likely make?

Accepted Answer

Added the coefficients without adjusting the exponents.

Question 10

Which of the following is the correct way to express the sum $$3.5 	imes 10$$^{-4}$$ + 2.1 	imes 10$$^{-5}$$ in scientific notation?

Accepted Answer

$$3.71 	imes 10$$^{-4}$$

Question 11

A medical test result is $$7.2 	imes 10^3$ units. If a correction of -1.5$$ 	imes $$10^2$$ units is applied, what is the corrected result?

Accepted Answer

$$7.05 	imes 10^3$ units

Question 12

If you are given $$4.0 	imes 10^6$ and 3.0$$ 	imes $$10^5$$, and you want to subtract the second from the first, what is the correct answer?

Accepted Answer

$$3.7 	imes 10^6$

Question 13

A scientist needs to add $$6.2 	imes 10$$^{-3}$$ and 4.8$$ 	imes $$10^{-4}. $$What is the sum in scientific notation?

Accepted Answer

$$6.68 	imes 10$$^{-3}$$

Question 14

Which of the following is the correct result for $$2.00 	imes 10^2$ - 5.0 	imes 10^1$?

Accepted Answer

$$1.50 	imes 10^2$

Question 15

A nurse needs to calculate the total dosage by adding $$3.5 	imes 10^2$ mg and 4.2$$ 	imes $$10^1 mg. $$What is the total dosage?

Accepted Answer

$$3.92 	imes 10^2$ mg

Question 16

If you are given $$5.0 	imes 10^4$ and 2.0$$ 	imes $$10^3$$, and you want to add them, what is the correct answer?

Accepted Answer

$$5.2 	imes 10^4$

Addition and Subtraction in Scientific Notation

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