## CHAPTER 1 BASIC HOMEWORK

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**Question 1**

Measurements are not exact. This is why significant figures are needed. What is the best you can say about the length of the green rectangle? (Feedback is given for each answer)

Select one:

**Explanation**

**Explanation**

This is the best answer. Someone else may say 1.23 or 1.25 cm. These are all good answers and better than 1.2 cm. Widget is loading comments… */ ]]>

**Question 2**

How many significant figures are in 95.4?

Help: Rules for Significant Figures

**Explanation**

**Explanation**

- All non-zero digits are significant. For example, 1.489 has 4 significant figures.

**Question 3**

How many significant figures are in 100.0000?

**Explanation**

**Explanation**

- Zeros are significant only when they occur:

- between two non-zero digits. For example, 309 has 3 sig. fig. and 2,004 has 4 sig. fig.
- to the right of a decimal point if preceded by a non-zero digit. For example 1.40 and 2.00 have 3 sig. fig. and 0.00170000 has 6 sig. fig. This is easy to tell in scientific notation–1.70000 x 10-3
- to the left of a decimal if preceded by a non-zero digit. For example, 500. has 3 sig. fig., but 500 has only one.

**Question 4**

How many significant figures are in 0.00076?

**Explanation**

**Explanation**

Zeros to the left of a number are not significant

**Question 5**

How many significant figures are in 1.00056? Review: Rules for Significant Figures

**Explanation**

**Explanation**

Zeros are significant only when they occur between two non-zero digits. For example, 309 has 3 sig. fig. and 2,004 has 4 sig. fig.

**Question 6**

How many significant figures are in 600700000?

**Explanation**

**Explanation**

- Zeros are significant only when they occur between two non-zero digits. For example, 309 has 3 sig. fig. and 2,004 has 4 sig. fig.
- To the left of a decimal if preceded by a non-zero digit. For example, 500. has 3 sig. fig., but 500 has only one.

**Question 7**

How many significant figures are in 44070.?

**Explanation**

**Explanation**

- Zeros are significant only when they occur between two non-zero digits. For example, 309 has 3 sig. fig. and 2,004 has 4 sig. fig.
- To the left of a decimal if preceded by a non-zero digit. For example, 500. has 3 sig. fig., but 500 has only one.

**Question 8**

Write 329600 in scientific notation to the correct number of significant figures. For example, 136 = 1.36 x 102 . In Moodle write 1.36e2 or 1.36E2. Help: Scientific Notation Examples

**Explanation**

**Explanation**

In scientific notation it is the number of digits used to write the number, e.g. 1.23 x 103 has 3 significant digits. Its value is 1,230(the decimal is moved 3 places to the right). 1.23 x 104 has 3 significant figures. Its value is 12,300. 1.2300 x 106 has 5 significant figures. Its value is 1,230,000. 1.03 x 10-2 has 3 significant figures. Its value is 0.0103.

**Question 9**

How many significant figures are in 1.0698 x 104? Review: Scientific Notation Examples

**Explanation**

**Explanation**

- Non-zero numbers are significant
- Zeros are significant only when they occur between two non-zero digits.

**Question 10**

How many significant figures are in 2.469 x 10-1?

**Explanation**

**Explanation**

- Non-zero numbers are significant

**Question 11**

What is 0.0024 in scientific notation? For example, 0.027 = 2.7 x 10-2. In Moodle write 2.7e-2 or 2.7E-2.

**Explanation**

**Explanation**

Moving the decimal to the right makes the nth power negative

**Question 12**

What is 174.23 rounded to the nearest whole number? Help: Rounding Examples

**Explanation**

**Explanation**

When rounding, look at the digit to the right of the place you want to round to. If it is 4 or smaller, round down. If it is 5 or greater, round up. Examples: 104.91 rounded to the nearest whole number is 105. 104.91 rounded to the nearest 10, it is 100 or 1.0 x 102. 47.04662 rounded to the nearest hundredth is 47.05. 47.04662 rounded to the nearest tenth is 47.0. 47.04662 rounded to the nearest ten is 50 or 5 x101. 47.04662 rounded to the nearest hundred is 0. **When doing calculations, wait until the end before rounding to avoid accumulative round-off error.**

**Question 13**

What is 337.3 rounded to 2 significant figures?

**Explanation**

**Explanation**

47.04662 rounded to the nearest ten is 50

**Question 14**

What is 60511 rounded to 3 significant figures?

**Explanation**

**Explanation**

Just round to the nearest thousand because nonzero numbers are significant and zeros between nonzero numbers are significant

**Question 15**

What is 9131.7 rounded to 1 significant figure?

**Explanation**

**Explanation**

Just round the first number on the left based on the number on the right.

**Question 16**

What is 4.24+ 31 to the correct number of significant figures? Help: Addition and Subtraction Examples

**Explanation**

**Explanation**

In addition and subtraction, you only know your information to the least accurate decimal place. For example, 2.2 + 15.251 = 17.451 = 17.5 because each number is known to at least the tenth decimal place. **Do not **use the number of significant figures in addition and subtraction.

Examples: 200 + 468 = 668 = 700 or 7 x 102 2.00 x 102 + 468 = 668 or 6.68 x 102 60 – 4.337 = 55.663 = 60 or 6 x 101 14 +330.4 -0.889 = 343.511 = 344 or 3.44 x 102

**Question 17**

What is 56.8 – 44.724 to the correct number of significant figures?

**Explanation**

**Explanation**

Least accurate number is 56.8 so round your final answer to the tenths!

**Question 18**

What is 736.4 +5 – 180.27 to the correct number of significant figures?

**Explanation**

**Explanation**

PEMDAS (#neverforget) 736.4 + 5 = 741.4 (least accurate number is 5) 741.4 – 180.27 = 561.13 ( least accurate number is 741) The final answer is simply 561

**Question 19**

What is 14 x 301.67 to the correct number of significant figures? Help: Multiplication and Division Examples

**Explanation**

**Explanation**

In multiplication and division, the correct number of significant figures in the answer is the same as the original number with the fewest. Examples:

12 x 468 = 5,616 = 5,600 or 5.6 x 103

6/207 = 0.0289… = 0.03 or 3 x 10-2

700 x 103 *15 = 1,081,500 = 1,000,000 or 1 x 106. Remember 700 has 1 sig. fig. Specific Answer ( I know this is what you wanted, but kiddos I can’t help ya on the test so you’re gonna have to put some effort in) 14 x 301.67 = 4223.38 ( 14 has the least amount of sig figs; 2)

**Question 20**

What is 10/21.52 to the correct number of significant figures?

**Explanation**

**Explanation**

Look above! (1 sig fig because 10 only has 1 and according to division and multiplication rules you go by the number with the least amount of sig figs)

**Question 21**

What is 11.81 x 0.15/984.7 to the correct number of significant figures?

**Explanation**

**Explanation**

- Identify order of operations [PEMDAS]
- Follow sig fig, rules for the individual operations
**Round off at the end. [DO IT FOR ME PLS]**- Review the rules before before you begin.

- Addition/Subtraction rules: Answer must have same # decimal places as the number with the fewest decimals; i. e. the number that is least accurate.
- Multiplication/Division rules: Answer must have same # sig figs as the number with with the lowest # of sig figs.

**PS: YOUR FINAL ANSWER CANNOT BE MORE ACCURATE THAN THE LEAST ACCURATE NUMBER IN THE EQN.!!!**

**Example # 1, with explanations in blue.** Solve: (14.76 – 14)/0.280

PEMDAS

Numerator: Subtraction rule , then division rule

(14.76 – 14) = 0.76

0.76 ( *1 sig fig*) /0.28 = 2.714

Correct answer = 2.714 rounded to 3

Solve 27.3 + 16.00/5 = 27.3 + 3.2 = 30.5

Order of operations: division first, followed by addition

16.00/5 = 3.2

27.3 + 16.00/5 = 27.3 + 3.2 = 30.5

Correct answer = 30.5 rounded to 31 or 3.1 x 101.

**Example 3: A bit more complicated.**

2000 – 14/3.2

Order of operations: Division, followed by subtraction

14/3.2 = 4.375 ( )

2000 – 4.375 = 1995.625 = 2000 ( rounded to 1 sig fig)

(2000 has 1 sig fig, no decimals, least accurate number, so the answer has to be reported to same # of figs as the least accurate number)

**Question 22**

What is 38.763/5.1 + 509.15 to the correct number of significant figures? Help: Complex Calculation Examples

**Explanation**

**Explanation**

PEMDAS (this is your main bae never forget) 38.763/5.1 = 7.6006 ( 2 sig figs according to the division rule) 7.6006 + 509.15 = 516.75 (remember to go the least accurate (+ rule)) Final Answer with rounding = 516.8

**Question 23**

What is (53+8601.8)/54 to the correct number of significant figures?

**Explanation**

**Explanation**

PEMDAS bbs (53 + 8601.8) = 8654.8 ( least accurate is 53 with no decimal place) 8654.8/54 = 160.27 (54 has only 2 sig figs) Dun dun dun the final answer is 160 ( who would known it’s not like it isn’t to the left or anything)