Scientific Notation

Question 1

Front

Answer 1

Back

Question 2

What is scientific notation?

Answer 2

A way to write numbers as a product of a coefficient (1 ≤ a < 10) and a power of ten: a × 10^n.

Question 3

What are the two parts of a number in scientific notation?

Answer 3

The coefficient (a number between 1 and 10) and the exponent on 10 (10^n).

Question 4

What does the exponent n represent in a × 10^n?

Answer 4

How many places the decimal moved: positive n = large number, negative n = small number.

Question 5

Why use scientific notation?

Answer 5

To represent very large or very small numbers concisely.

Question 6

What range must the coefficient be in scientific notation?

Answer 6

It must be ≥ 1 and < 10.

Question 7

How do you convert a large number to scientific notation?

Answer 7

Move the decimal after the first nonzero digit; exponent = digits moved (positive).

Question 8

How do you convert a small decimal to scientific notation?

Answer 8

Move the decimal right until one nonzero digit remains; exponent = moves (negative).

Question 9

Convert 4,500 to scientific notation.

Answer 9

4.5 × 10^3

Question 10

Convert 0.00032 to scientific notation.

Answer 10

3.2 × 10^-4

Question 11

Convert 120,000,000 to scientific notation.

Answer 11

1.2 × 10^8

Question 12

Convert 4.5 × 10^3 to standard form.

Answer 12

4500

Question 13

Convert 9.1 × 10^-3 to standard form.

Answer 13

0.0091

Question 14

Convert 3.45 × 10^2 to standard form.

Answer 14

345

Question 15

Convert 1.0 × 10^0 to standard form.

Answer 15

1

Question 16

How does scientific notation show significant figures?

Answer 16

Only digits in the coefficient are significant.

Question 17

Is 0.56 × 10^5 valid scientific notation?

Answer 17

No. Correct form: 5.6 × 10^4.

Question 18

Round 3.14159 × 10^2 to 3 significant figures.

Answer 18

3.14 × 10^2

Question 19

Which is larger: 6.3 × 10^5 or 5.9 × 10^6?

Answer 19

5.9 × 10^6

Question 20

Rule for multiplying scientific notation?

Answer 20

(a × 10^m)(b × 10^n) = (ab) × 10^(m+n).

Question 21

Compute (2.0 × 10^3)(3.0 × 10^4).

Answer 21

6.0 × 10^7

Question 22

Rule for dividing scientific notation?

Answer 22

(a × 10^m)/(b × 10^n) = (a/b) × 10^(m−n).

Question 23

Compute (8.4 × 10^6) ÷ (2.1 × 10^2).

Answer 23

4.0 × 10^4

Question 24

Rule for adding/subtracting scientific notation?

Answer 24

Rewrite so exponents match, then add/subtract coefficients.

Question 25

Compute 3.2 × 10^5 + 7.0 × 10^4.

Answer 25

3.9 × 10^5

Question 26

Compute 1.5 × 10^-3 − 2.0 × 10^-4.

Answer 26

1.3 × 10^-3

Question 27

Rule for raising to a power in scientific notation?

Answer 27

(a × 10^n)^k = a^k × 10^(nk).

Question 28

Compute (3.0 × 10^2)^2.

Answer 28

9.0 × 10^4

Question 29

Compute √(9.0 × 10^6).

Answer 29

3.0 × 10^3

Question 30

What is order of magnitude?

Answer 30

The power of ten closest to the number.

Question 31

Which has greater order of magnitude: 7.9 × 10^8 or 1.2 × 10^9?

Answer 31

1.2 × 10^9

Question 32

Correct this: 0.00056 = 0.056 × 10^-3

Answer 32

Correct: 5.6 × 10^-4

Question 33

Fix: 4.5 × 10^3 + 3.0 × 10^2

Answer 33

4.8 × 10^3

Question 34

True or False: 10^-3 < 10^-5

Answer 34

False, 10^-3 = 0.001 which is greater.

Question 35

Convert 0.0000079 to scientific notation.

Answer 35

7.9 × 10^-6

Question 36

Convert 85,000,000 to scientific notation.

Answer 36

8.5 × 10^7

Question 37

Convert 4.0 × 10^-5 to standard form.

Answer 37

4.0e-05

Question 38

Multiply (4.0 × 10^-2)(2.5 × 10^3).

Answer 38

1.0 × 10^2

Question 39

Divide (9.0 × 10^5) ÷ (3.0 × 10^2).

Answer 39

3.0 × 10^3

Question 40

Add 6.0 × 10^4 + 2.5 × 10^5.

Answer 40

3.1 × 10^5

Question 41

Order these: 3.1 × 10^-2, 2.9 × 10^-3, 4.0 × 10^-1

Answer 41

2.9 × 10^-3 < 3.1 × 10^-2 < 4.0 × 10^-1