Unit 1 Measurement Review

Unit 1 Measurement Review

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Significant Figures

1. All nonzero digits are significant. 
2. Sandwiched zeros are significant.
3. ONLY trailing zeros in a decimal number are significant. 
4. Leading zeros are NOT significant.
5. All numbers before x10 in scientific notation are significant. 

1. All nonzero digits are significant

• Ex: 120 = 2 sig figs

• Ex: 652,000 = 3 sig figs

• Ex: 40 = 1 sig figs

2. Sandwiched zeros are significant. 

• Ex: 205 = 3 sig figs

• Ex: 1006 = 4 sig figs

• Ex: 101,000 = 3 sig figs

3. Trailing zeros are not significant UNLESS in a decimal number. 

• Ex: 100 = 1 sig fig

• Ex: 100. = 3 sig fig

• Ex: 20.00 = 4 sig figs

4. Leading zeros are NOT significant. 

• Ex: 0.0025 = 2 sig figs

• Ex: 0.0003710 = 4 sig figs

• Ex: 0.0800 = 3 sig figs

5. All numbers before x10 in scientific notation are signigicant. 

• Ex: 3.0 x 10^3 = 2 sig figs

• Ex: 1.560 x 10^-2 = 4 sig figs

• Ex: 4 x 10^7 = 1 sig figs

Multiple Choice

Determine the significant figures in the following measurement: 205. 8

• 3

• 4

• 2

Multiple Choice

Determine the significant figures in the following measurement: 0.00745

• 5

• 6

• 3

Multiple Choice

Determine the significant figures in the following measurement: 21000

• 5

• 1

• 2

Multiple Choice

Determine the significant figures in the following: 3.105 x10⁴

• 4

• 5

• 3

Multiple Choice

Determine the significant figures in the following measurement: 620.0

• 3

• 2

• 4

Fill in the Blank

3.20 x 10⁵ = _____ significant figures

Fill in the Blank

56.70 = ______ significant figures

Fill in the Blank

0.00830 = ____ significant figures

Scientific Notation

How we write very big, and very small numbers! Also useful to show our significant figures. 

Steps to write in scientific notation:

• Step 1: Determine if we will need a negative or positive exponent. 

• Ex: 540,000 --> greater than 1, our exponent will be positive. 

• Ex: .0005400 --> less than 1, our exponent will be negative. 

Step 2: Determine the significant figures. 

• Ex: 540,000 = 2 sig figs

• Ex: 0.0005400 = 4 sig figs

Step 3: Count your placeholders. 

• You can determine the placeholders by the amount of spaces you will move your decimal. 

• Count down until you have a number between 1 and 9. 
  
  

• Ex: Number with positive exponent move to left

• 540,000 --> 5.40000 --> 5 spaces --> exponent will be positive 5. 
  
  

• Now write including only sig figs and x 10:

• 5.4 x 10^5

Step 3: Count your placeholders. 

• You can determine the placeholders by the amount of spaces you will move your decimal. 

• Count down until you have a number between 1 and 9. 
  
  

• Ex: Number with negative exponent move to right

• 0.0005400 --> 005.400 --> 4 spaces --> exponent will be negative 4. 
  
  

• Now write including only sig figs and x 10:

• 5.400 x 10^-4

Multiple Choice

Write the following number in scientific notation: 142.63

• 1.4263 x 10^-2

• 1.43 x 10²

• 1.4263 x 10²

Multiple Choice

Write the following in scientific notation: 0.00125

• 1.25 x 10^-3

• 1.25 x 10³

• 001.25 x 10^-3

Multiple Choice

Write the following in scientific notation: 0.000337

• 3.37 x 10^-3

• 3.4 x 10^-4

• 3.37 x 10^-4

Multiple Choice

Write the following in scientific notation: 150,000

• 1.50 x 10⁵

• 1.5 x 10⁵

• 1.50 x 10^-5

Step 1: Writing in Standard (expanded) form

• Determine if you have a number greater 1 --> positive exponent

• Ex: 4.20 x 10^5 

• Determine if your number issmaller than 1 --> negative exponent

• Ex: 4.20 x 10^-3

Step 2: Direction you need to move decimal

• Positive exponent = right

• Negative exponent = left
  
  
  

Step 3: Move the decimal the same number as the exponent. 

• Ex: 4.20 x 10^5 = 420000 

• Ex: 4.20 x 10^-3 = .00420 

• *Notice that whether the decimal moved left or right any blank spaces were filled with zeros. 

Multiple Choice

Write in standard form: 8.64 x 10⁴

• 86400

• 8640000

• .000864

Multiple Choice

Write in standard form: 4.5 x 10^-3

• .0045

• .00450

• .045

Multiple Choice

Write in standard form: 1.63 x 10⁶

• 163,000

• .00000163

• 1,630,000

Multiple Choice

Write in standard form: 8.91 x 10^-1

• .0891

• .891

• 89.1

Metric Conversions

We can easily convert from one unit in metric to another by moving the decimal point. 

Base Units:

Meters - m
Liters - L
Grams - g

Using the chart to convert

Find your starting unit

Ex: 25 cm = ____ m
- count the spaces from starting unit to ending unit. 
- move the decimal in the same direction the same amount of spaces.

25 cm = .25 m --> you moved 2 spaces to the left

Multiple Choice

1000 mL= _______ L

• 1 L

• 10 L

• .1 L

Multiple Choice

3 kg = _______ g

• 300

• 3000 g

• 30

Multiple Choice

45 mm = ________ cm

• 450 cm

• .45 cm

• 4.5 cm

Multiple Choice

85.2 g = ______ kg

• .0852 kg

• .852 kg

• 8.52 kg

Multiple Choice

25 m = ______ km

• 250 km

• .25 km

• .025 km

Multiple Choice

3 L = _____ mL

• 3.00 mL

• 30000 mL

• 3000 mL

Density

Measurement of mass per volume. 

Tip: You can use units to help you identify the variable given in a problem. 

• mass --> g 

• volume --> mL or L or cm^3

• density --> g/mL or g/L or g/cm^3

Multiple Choice

What is the density of a substance with a mass of 12.0 g and volume of 120.0 mL?

• 1.00 g/mL

• 0.01 g/mL

• 0.100 g/mL

Multiple Choice

What is the volume of a substance with a mass of 33 g and density of 11 g/mL?

• 3.0 mL

• 3.1 mL

• 30 mL

Multiple Choice

What is the mass of a substance with a volume of 150 cm³ and a density of 3.5 g/cm³?

• 525 g

• 500 g

• 530 g

Multiple Choice

What is the density of a substance of an object with a mass of 150. g and a volume of 10.0 cm³

• 15.0 g/cm³

• 1.50 g/cm³

• 15 g/cm³

Percent Error

Helps us compare our measured values to the true values. 

Percent Error

True value = actual, known, accepted value

measured = experimental, calculated, estimated value

Multiple Choice

Determine the percent error if when the experimental value is 72.5 g and the true value is 72.7 g.

• .1%

• .2%

• .3%

Multiple Choice

What is the percent error when the measured value is 2.3 cm and the actual value is 2.8 cm?

• 20%

• 18%

• 17.8%