Name:_____________
Date:____________
Multiplying by Powers of 10 and Scientific Notation Weekly Homework
What is my expectation for this homework?





This homework is due on Friday at the beginning of class
The answers the homework will be find on the 8th grade Website (8mics.weebly.com) on
the HOMEWORK ANSWERS tab under the MATH menu
I will take 5 minutes every day during class to take questions
If you lose this sheet, it will be posted on the website under the CLASSWORK PAGES
tab under the MATH menu.
If you do not have internet, you need to come to me during SOAR to check your answers.
______________________________________________________________________________
Review of the Laws of Exponents
Directions: Simplify the following. Express using positive exponents
1. 4−3 ∙ 45 = 𝟒−𝟑+𝟓 = 𝟒𝟐
2.
−10−3
−104
𝟏
= −𝟏𝟎−𝟑−𝟒 = −𝟏𝟎−𝟕 = −𝟏𝟎𝟕
3. (5−6 )−7 = 𝟓−𝟕∙−𝟔 = 𝟓𝟒𝟐
4.
5−3 ∙42
𝟒𝟔
= 𝟒𝟐−(−𝟒) ∙ 𝟓−𝟑−𝟎 = 𝟒𝟔 ∙ 𝟓−𝟑 = 𝟓𝟑
4−4 ∙50
__________________________________________________________
Monday Night: Multiplying by Powers of 10 and Writing in Scientific Notation
Directions: Find the Standard Form
1.
2.
3.
4.
1.456 ∙ 105 = 𝟏𝟒𝟓, 𝟔𝟎𝟎
0.6573 ∙ 102 = 𝟔𝟓. 𝟕𝟑
125.49876 ∙ 10−3 = 𝟎. 𝟏𝟐𝟓𝟒𝟗𝟖𝟕𝟔
3,456.987 ∙ 10−7=0.0003456987
Directions: Write the following in Scientific Notation. Explain how you got your power of 10.
1. 123.45
a. Scientific Notation: 1.2345 × 102
b. Explanation of Power of 10: The first part of the Scientific Notation needs to
be between 1 and 10. So to make 123.45 into a number between 1 and 10 we
need to move the decimal point 2 places to the left, which gives us the positive
2 for the exponent
2. 0.4567
a. Scientific Notation: 4.567 × 10−1
b. Explanation of Power of 10: We need to make 0.4567 into a number between 1
and 10. To do that, we move the decimal one place to the right, which gives
us the negative 1 for the exponents
3. 123.456 ∙ 102
a. Scientific Notation: 1.23456 × 102 × 102 = 1.23456 × 104
b. Explanation of Power of 10: Our question is NOT written in scientific notation
because 123.456 is not between 1 and 10. To make it a number between 1 and
10, we move the decimal 2 places to the left. This gives us 1.23456 being
multiplied by 10 with an exponent of 2. By the Law of Multiplying Like
Bases, we can multiply the two bases of 10 together by keeping the 10 and
adding the exponents together. The addition of the exponents gets us the 4 as
the exponent on the 10.
Tuesday Night: Operating with Scientific Notation
Directions: Find each sum, difference, product, or quotient. Write your answers in Scientific
Notation
1. (1.25 ∙ 105 ) + (5.35 ∙ 106 )
a. 𝟏. 𝟐𝟓 ∙ 𝟏𝟎𝟓 = 𝟏𝟐𝟓𝟎𝟎𝟎
b. 𝟓. 𝟑𝟓 ∙ 𝟏𝟎𝟔 = 𝟓𝟑𝟓𝟎𝟎𝟎𝟎
c. 5350000+125000=5,375,000
2. (6.3 ∙ 103 ) + (7.7 ∙ 103 )
a. (𝟔. 𝟑 ∙ 𝟏𝟎𝟑 ) = 𝟔𝟑𝟎𝟎
b. (𝟕. 𝟕 ∙ 𝟏𝟎𝟑 ) = 𝟕𝟕𝟎𝟎
c. 6300+7700=14,000
d. 1.4 ∙ 104
3. (3.67 ∙ 106 ) − (4.56 ∙ 107 )
a. 𝟑. 𝟔𝟕 ∙ 𝟏𝟎𝟔 = 𝟑𝟔𝟕𝟎𝟎𝟎
b. 𝟒. 𝟓𝟔 ∙ 𝟏𝟎𝟕 = 𝟒𝟓𝟔𝟎𝟎𝟎𝟎𝟎
c. 𝟒. 𝟓𝟔 ∙ 𝟏𝟎𝟕
4. (5.8 ∙ 102 ) − (3.8 ∙ 102 )
a. 𝟓. 𝟖 ∙ 𝟏𝟎𝟐 = 𝟓𝟖𝟎
b. 𝟑. 𝟖 ∙ 𝟏𝟎𝟐 = 𝟑𝟖𝟎
c. 580+380=960
d. 𝟗. 𝟔 ∙ 𝟏𝟎𝟐
5. (6.0 ∙ 104 ) ∙ (1.5 ∙ 10−2 )
a. 𝟔 ∙ 𝟏. 𝟓 ∙ 𝟏𝟎𝟒 ∙ 𝟏𝟎−𝟓 = 𝟗 ∙ 𝟏𝟎𝟒+(−𝟓) = 𝟗 ∙ 𝟏𝟎−𝟏
6. (6.6 ∙ 104 ) ÷ (2.3 ∙ 10−3 )
a. (𝟔. 𝟔 ÷ 𝟐. 𝟑) ∙ (𝟏𝟎𝟒 ÷ 𝟏𝟎−𝟑 ) = 𝟐. 𝟖𝟕 ∙ 𝟏𝟎𝟒−(−𝟑) = 𝟐. 𝟖𝟕 ∙ 𝟏𝟎𝟒+𝟑 = 𝟐. 𝟖𝟕 ∙ 𝟏𝟎𝟕
Wednesday Night: Word Problems with Scientific Notation
1. In 2010, Facebook had 5 million users. In 2014, 3 million more people signed up to
access the site. How many people in total used Facebook in 2014? Express your answer
in Scientific Notation
a. To find our answer, we are going to add together the number of users.
b. 5 million + 3 million=8 million
c. 8 million in scientific is 𝟖 ∙ 𝟏𝟎𝟔
d. There was a total of 𝟖 ∙ 𝟏𝟎𝟔 people who signed up for Facebook
2. A bank starts the day with 2.95 × 105 dollars in the vault. At the end of the day, the bank
has 10.5 × 105 dollars in the vault. How much more money is in the vault at the end of
the day than there was in the morning?
a. To find our answer, we are going to subtract the money at the start of the
day from the money at the end of the day.
b. 10.5 × 𝟏𝟎𝟓 − 𝟐. 𝟗𝟓 × 𝟏𝟎𝟓
c. 10.5 × 𝟏𝟎𝟓 = 𝟏𝟎𝟓𝟎𝟎𝟎𝟎
d. 𝟐. 𝟗𝟓 × 𝟏𝟎𝟓 = 𝟐𝟗𝟓𝟎𝟎𝟎
e. 1050000-295000=75500
f. There was $755,000 more in the bank at the end of the day
3. In 2005, 8.1 ∙ 1010 text messages were sent in the United States. In 2010, the number of
texts messages sent jumped to 1,810, 000, 000, 000. About how many times as great was
the number of text messages sent in 2010 than 2005.
a. We want to turn the number of text messages sent in 2010 into scientific
notation. 1,810,000,000,000=𝟏. 𝟖𝟏 ∙ 𝟏𝟎𝟏𝟐
b. To find our answer, we divide the number of text messages in 2010 by the
number of text messages in 2005
c. 𝟏. 𝟖𝟏 ∙ 𝟏𝟎𝟏𝟐 ÷ 𝟖. 𝟏 ∙ 𝟏𝟎𝟏𝟎 = (𝟏. 𝟖𝟏 ÷ 𝟖. 𝟏) ∙ (𝟏𝟎𝟏𝟐 ÷ 𝟏𝟎𝟏𝟎 ) = 𝟎. 𝟐𝟐 ∙
𝟏𝟎𝟏𝟐−𝟏𝟎 = 𝟎. 𝟐𝟐 ∙ 𝟏𝟎𝟐 = 𝟐𝟐
d. The number of text messages sent in 2010 was 22 times as great as the
number of text messages sent in 2005.
4. Everyday 2.53 ∙ 104 songs are downloaded off of Spotify. How many songs will be
downloaded off of Spotify in a year?
a. A year has 365 days and 365 in Scientific Notation is 𝟑. 𝟔𝟓 ∙ 𝟏𝟎𝟐
b. We are going to multiply the number of songs per day by the number of days
in a year.
c. (𝟐. 𝟓𝟑 ∙ 𝟏𝟎𝟒 ) ∙ (𝟑. 𝟔𝟓 ∙ 𝟏𝟎𝟐 ) = 𝟐. 𝟓𝟑 ∙ 𝟑. 𝟔𝟓 ∙ 𝟏𝟎𝟒 ∙ 𝟏𝟎𝟐 = 𝟗. 𝟐𝟑𝟒𝟓 ∙ 𝟏𝟎𝟒+𝟐 =
𝟗. 𝟐𝟑𝟒𝟓 ∙ 𝟏𝟎𝟔 = 𝟗𝟐𝟑𝟒𝟓𝟎𝟎
d. 9,234,500 songs will be downloaded from Spotify in one year.