Scientific Notation
Write 1.67 x 104 in expanded form.
16 700
what is 100 written in powers of 10
102
write the expanded form of 57
5 x 5 x 5 x 5 x 5 x 5 x 5
Write the number 150 in expanded notation using powers of ten.
1x102 + 5 x 10
What is the difference between a terminating and repeating decimal? Give an example for each.
A terminating decimal ends, for example 0.5. A repeating decimal repeats the same number but goes on forever such as 0.3333333...
Write 156 000 in scientific notation.
1.56 x 105
104
Evaluate 73
343
Write the number 1456 in expanded notation using powers of ten.
1 x 103 + 4 x 102 + 5 x 10 + 6
Define an irrational number. Give an example.
An irrational number cannot be put in fraction form. It is a decimal number that is constantly changing and never ending. An example is pi or square root of 2.
What does a negative exponent indicate in scientific notation?
A negative exponent indicates a very small number.
What is 100 000 000 in powers of ten
108
Evaluate 125
248832
Write the number 25 627 in expanded notation using powers of ten.
2 x 104 + 5 x 103 + 6 x 102 + 2 x 10 + 7
A factory produces 8,000 pencils every day.
How many pencils does the factory produce in 10 days? Write this number in powers of ten.
If each pencil weighs about 1 × 10⁻² kilograms, what is the total weight of all the pencils produced in 10 days? Give your answer in scientific notation.
1. 8,000×10=80,000 pencils which is 8 x 104
2. 800 kg or 8 x 102
What is the expanded form of 7.313 x 10-5
0.00007313
1011
Evaluate (122-120)2
576
Write the number 351 673 in expanded notation using powers of ten.
3 x 105 + 5 x 104 + 1 x 103 +6 x 102+ 7x10+ 3
A spaceship travels through space and collects data from two distant stars.
The first star is 4,200,000,000,000 kilometers away from Earth.
The second star is 7,500,000 kilometers away from a nearby planet.
Your task:
Convert both distances into scientific notation.
Which distance is greater and by how many powers of 10?
First Star:
We move the decimal point 12 places to the left to write this in scientific notation:
4,200,000,000,000=4.2×1012
Second Star:
We move the decimal point 6 places to the left:
7,500,000= 7.5×106
The first star is farther by 6 powers of 10.
What is the expanded form of 1.81 x 10-4
0.000181
What is 1 000 000 000 000 000 000 000 in powers of ten
1021
Evaluate ((33+5)-(23))3
13 824
Write the number 891 745 732 081 in expanded notation using powers of ten.
8 x 1011 + 9 x 1010+ 1 x 109 +7 x 108+ 4 x 107 + 5 x 106+ 7 x 105+ 3 x 104+ 2 x 103 + 8 x 10 + 1
A single water molecule has a mass of about
0.0000000000299 grams.
A grain of sand weighs approximately
0.00044 grams.
Your Tasks:
Convert both masses into scientific notation.
How many times heavier is a grain of sand compared to a water molecule?
Water molecule: 2.99×10-11grams
Grain of sand: 4.4×10−4grams
It is approximately 1.47 x 107 grams heavier