TRS 92
Day 5 Homework
Practice New Skills: Scientific Notation and Multiplying Exponents
1. Complete the table by converting between standard and scientific notation and the verbal
description. An example is given in the first row.
Verbal Description
Standard Notation
Scientific
Notation
Example 2.3 billion
2,300,000,000
2.3 x 109
a)
3 billion, 250 million
b)
62,000,000
c)
5.6 x 108
d)
5 trillion
2. Refer back to your Day 3 homework. Record the population of each continent in scientific
notation rounding to two decimal places. Then convert the area of the continent to
scientific notation.
Continent
Population in
Scientific Notation
Europe
Area in Standard
Notation (km2)
9,938,000
Asia
43,998,000
Africa
29,800,000
North America
24,250,000
South America
18,840,000
Oceania
7,690,000
Area in Scientific
Notation (km2)
3. Identify the base that is being raised to the 5th power for each expression.
a) 3x5
b) (3x)5
c) 4(3x)5
d) 3x( x)5
Base:
Base:
Base:
Base:
TRS 92
Simplify each expression.
4. 5 x(2 x3 y ) =
Day 5 Homework
5.
(6 x5 )(3x3 y 6 )(2 y 3 ) =
6.
2 4
x y (5 x 6 y 2 ) =
3
Use the rule for multiplying bases to simplify the following problems in scientific notation.
Remember to be sure your answer is in scientific notation. Show your work.
7. (1.2 x 1010) (3.0 x 107)
8. (5.2 x 104) (6.0 x 108)
Writing About Math
Writing about math serves several purposes:
 Research shows that students learn and remember concepts better when they write
about them.
 Writing or explaining a concept helps you to assess your own understanding.
 Writing about a process in a logical, clear and concise manner is an important skill and
takes a great deal of practice. This type of writing is often called technical writing. The
writing in this course will help you develop this skill and prepare you for the type of
writing you will use in many future courses and situations in your future career and life.
Refer back to the Day 3 Activity and HW, Introduction to Unit Analysis. Review how the
examples are explained. This is a 2-column form in which the mathematical work is shown in
one column with explanations next to it. Also notice the following characteristics:
 The work is shown step-by-step.
 Each step is explained completely with both a description of what is done and why.
 The explanations use correct vocabulary like numerator, denominator, multiply, etc.
 The explanations do not use personal pronouns and pronouns such as it, they are
limited.
Here are some more examples demonstrating common errors in technical writing.
Use short, complete sentences.
Too long and repetitive:
When adding fractions, you have to have the
same denominator for all the fractions you
have because you can’t add them without it.
Incomplete sentence:
Need a common denominator.
Better
To add fractions, find a common denominator.
TRS 92
Day 5 Homework
Use correct mathematical vocabulary.
Incorrect vocabulary:
If you times the top number and the bottom
number by the same number, you get the
same fraction.
Use precise language. Avoid pronouns.
Unclear what pronouns represent:
4x and 8x are like terms because they are the
same. It’s not like terms if they’re different like
with a different power or letter.
Better
Multiplying the numerator and the denominator
by the same number does not change the
value of the fraction. The fractions are
equivalent.
Better
4x and 8x are like terms because the variables
are the same and have the same power in
both expressions. 4x and 8x2 are not like
terms because the powers are different. 4x
and 8y are not like terms because the
variables are different.
Use specific examples to explain concepts. Put space between parts of the problem.
Hard to understand:
Better
To find the reciprocal of a number, turn it over. The reciprocal of a number reverses the
If it’s a whole number use 1 in the bottom. If
numerator and denominator. So the reciprocal
it’s mixed, you have to convert it first.
2
3
of
is
.
3
2
To find the reciprocal of a whole number, write
the whole number with a denominator of 1
first. 5 
5
1
so the reciprocal of 5 is .
1
5
For mixed numbers, convert the number to an
improper fraction first. 3
reciprocal is
3 15

so the
4 4
4
.
15
Writing Prompt #1
Use the guidelines above to write an explanation and solution for the following problem.
Vocabulary that you should use includes, but is not limited to: denominator, numerator, multiply.
Think about writing the explanation for someone who has never learned to add fractions before.
3 4

8 5
You may write your work neatly on the back of this page or handwrite or type your work on a
separate piece of paper.