Name: Date:
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.
1. 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.
1. The Burj Khalifa is 828,000,000 micrometers tall. How is this value written in scientific notation in
Gizmo™? 8.2 * 10^8
the
2. In a value, any non-zero digit is considered a significant digit. (Zeroes may or may not be
What is the minimum number of significant digits in 828
828,000,000?
significant.)
, Get the Gizmo ready:
Activity A: ● Select Metric units only and Distance from the
Conversion menu. Make sure Show result is
Scientific notation off.
● Click Next until you reach the question
about Proxima Centauri.
Question: How can you convert numbers into and out of scientific notation?
1. 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.
2. 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
8.35 × 107 8.3 500 83 500 000.0 83,500,000
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.
Place new decimal Scientific
Standard form Count digits
point notation
123 456
3,700,000 3.700 000 3.700 3.7 × 106
000
Practice this with the two numbers below:
8,200,000 8.2*10^6 50,880,000,000,000 5.088*10^13
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.
1. 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.
1. The Burj Khalifa is 828,000,000 micrometers tall. How is this value written in scientific notation in
Gizmo™? 8.2 * 10^8
the
2. In a value, any non-zero digit is considered a significant digit. (Zeroes may or may not be
What is the minimum number of significant digits in 828
828,000,000?
significant.)
, Get the Gizmo ready:
Activity A: ● Select Metric units only and Distance from the
Conversion menu. Make sure Show result is
Scientific notation off.
● Click Next until you reach the question
about Proxima Centauri.
Question: How can you convert numbers into and out of scientific notation?
1. 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.
2. 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
8.35 × 107 8.3 500 83 500 000.0 83,500,000
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.
Place new decimal Scientific
Standard form Count digits
point notation
123 456
3,700,000 3.700 000 3.700 3.7 × 106
000
Practice this with the two numbers below:
8,200,000 8.2*10^6 50,880,000,000,000 5.088*10^13
