Student Exploration-Unit Conversions 2 –Scientific Notation and
Significant Digits
[Note to teachers and students: This lesson is designed to be a follow-up to the Unit Conversions Student Exploration sheet
The same Gizmo is used for both activities.]
Directions: Follow the instructions to go through the simulation. Respond to the questions and prompts in the orange boxes.
Vocabulary: resolution, scientific notation, significant digits
Prior Knowledge Questions (Do these BEFORE using the Gizmo.)
Philip measures a room using his feet. (His feet are each about a foot long.) He estimates the room measures about ten
and a half feet by thirteen and a half feet. He calculates the room’s area to be: 10.5’ × 13.5’ = 141.75 ft2.
Which do you think is the best description of the area of the room? Highlight your choice.
A. The room’s area is exactly 141.75 ft2. B. The room’s area is about 142 ft2.
2. Explain your choice: I chose that answer because it the answer but rounded up to 3 sig fig
Gizmo Warm-up
When scientists report a value, they have to take several things into consideration. Sometimes values are very large or
small. In this case, scientists can use shorthand called scientific notation to report the value.
Scientists also must consider how precise their value is. The precision of a measurement can be shown by the number of
significant digits in the value.
To begin, check that the Burj Khalifa question is shown. Drag the three tiles shown below to determine the tower’s height in
micrometers. The answer is given in scientific notation.
The Burj Khalifa is 828,000,000 micrometers tall. How is this value written in scientific notation in the
Gizmo™? 8.2 * 10^8
In a value, any non-zero digit is considered a significant digit. (Zeroes may or may not be significant.)
What is the minimum number of significant digits in 828,000,000? 828
, Get the Gizmo ready:
Activity A: Scientific Select Metric units only and Distance from the
notation Conversion menu. Make sure Show result is off.
Click Next until you reach the question aboutProxima
Centauri.
Question: How can you convert numbers into and out of scientific notation?
Observe: Some of the problems in this Gizmo involve very small or very large quantities. Look at the bottom three Unit
Conversion Tiles. What do you notice in the numerator?
The number is low
The numbers in the numerators are written in scientific notation. In scientific notation, a number is converted to the product
of a number between 1 and 10 and a power of 10. For example, 1,000,000 is written as 1.0 • 106. The first part of this
number is called the coefficient. The second part is called the base.
Convert: To convert a number written in scientific notation into a standard number, first look at the exponent on the base. If
it is positive, move the decimal point on the coefficient to the right as many times as the exponent indicates, as shown
below:
Look at exponent Count digits Move decimal point Standard form
1 234 567
8.3 500 000
8.35 × 107 83 500 000.0 83,500,000
Practice converting the two numbers below into standard form:
1.0 • 109 = 10000000000 6.72 • 1012 = 672,000,000,000,000.
You can perform this process in reverse to convert numbers in standard form into scientific notation. The number of times
you move the decimal point to the left will be equal to the exponent on your base.
Remember there should be only one digit to the left of the decimal point in scientific notation.
Standard form Place new decimalpoint Count digits Scientificnotation
123 456
3.700 000
3,700,000 3.700 000 3.7 × 106
Practice this with the two numbers below:
8,200,000 = 8.2*10^6 50,880,000,000,000 = 5.088*10^13
Significant Digits
[Note to teachers and students: This lesson is designed to be a follow-up to the Unit Conversions Student Exploration sheet
The same Gizmo is used for both activities.]
Directions: Follow the instructions to go through the simulation. Respond to the questions and prompts in the orange boxes.
Vocabulary: resolution, scientific notation, significant digits
Prior Knowledge Questions (Do these BEFORE using the Gizmo.)
Philip measures a room using his feet. (His feet are each about a foot long.) He estimates the room measures about ten
and a half feet by thirteen and a half feet. He calculates the room’s area to be: 10.5’ × 13.5’ = 141.75 ft2.
Which do you think is the best description of the area of the room? Highlight your choice.
A. The room’s area is exactly 141.75 ft2. B. The room’s area is about 142 ft2.
2. Explain your choice: I chose that answer because it the answer but rounded up to 3 sig fig
Gizmo Warm-up
When scientists report a value, they have to take several things into consideration. Sometimes values are very large or
small. In this case, scientists can use shorthand called scientific notation to report the value.
Scientists also must consider how precise their value is. The precision of a measurement can be shown by the number of
significant digits in the value.
To begin, check that the Burj Khalifa question is shown. Drag the three tiles shown below to determine the tower’s height in
micrometers. The answer is given in scientific notation.
The Burj Khalifa is 828,000,000 micrometers tall. How is this value written in scientific notation in the
Gizmo™? 8.2 * 10^8
In a value, any non-zero digit is considered a significant digit. (Zeroes may or may not be significant.)
What is the minimum number of significant digits in 828,000,000? 828
, Get the Gizmo ready:
Activity A: Scientific Select Metric units only and Distance from the
notation Conversion menu. Make sure Show result is off.
Click Next until you reach the question aboutProxima
Centauri.
Question: How can you convert numbers into and out of scientific notation?
Observe: Some of the problems in this Gizmo involve very small or very large quantities. Look at the bottom three Unit
Conversion Tiles. What do you notice in the numerator?
The number is low
The numbers in the numerators are written in scientific notation. In scientific notation, a number is converted to the product
of a number between 1 and 10 and a power of 10. For example, 1,000,000 is written as 1.0 • 106. The first part of this
number is called the coefficient. The second part is called the base.
Convert: To convert a number written in scientific notation into a standard number, first look at the exponent on the base. If
it is positive, move the decimal point on the coefficient to the right as many times as the exponent indicates, as shown
below:
Look at exponent Count digits Move decimal point Standard form
1 234 567
8.3 500 000
8.35 × 107 83 500 000.0 83,500,000
Practice converting the two numbers below into standard form:
1.0 • 109 = 10000000000 6.72 • 1012 = 672,000,000,000,000.
You can perform this process in reverse to convert numbers in standard form into scientific notation. The number of times
you move the decimal point to the left will be equal to the exponent on your base.
Remember there should be only one digit to the left of the decimal point in scientific notation.
Standard form Place new decimalpoint Count digits Scientificnotation
123 456
3.700 000
3,700,000 3.700 000 3.7 × 106
Practice this with the two numbers below:
8,200,000 = 8.2*10^6 50,880,000,000,000 = 5.088*10^13
