Converting Numbers
What does it mean for a number to be written in scientific notation?
What is it is written as a×10n where 1≤a<10 and n is an integer?
What does the exponent tell you in scientific notation?
DOUBLE POINTS (x2): How do you know whether the number is less than one?
What is how many places the decimal moves (place value)
DOUBLE POINTS (X2): base is a fraction: 2.3x1/102 = 0.023
OR exponent is negative: 4.5x10-3 = 0.0045
When a number is written in scientific notation with a fractional exponent like 1.2 x 1/10n, is the number less than or greater than 1? How does this affect where you place the decimal?
What is the number is less than 1; the decimal moves left?
What does the phrase “A is ___ times as many as B” mean in math?
It means to divide A by B to see how many times bigger A is compared to B.
A divided by B OR A/B OR A÷B OR to divide A by B
What must be true about the powers of 10 before adding OR subtracting in scientific notation?
What is the powers (exponents) must be the same.
Write 4.6×103 in standard form.
What is 4,600?
Rewrite the following numbers in order from least to greatest:
5.3×104, 48,000, 4.8×103, 5300
What is 4.8×103, 5300, 48,000, 5.3×104?
All Standard Form: 4,800, 5,300, 48,000, 53,000
All Scientific Notation: 4.8×103, 5.3x103, 4.8×104, 5.3x104.
Which is bigger: 6.0×106 OR 3.0×104? How many times bigger?
What is 6.0×106 is 200 times bigger than 3.0×104?
600/3=200
In 1900, a population was 8.0×105. Today it’s 2.4×107. How many times larger is today's population?
What is 30 times larger?
240/8=30
Solve and show answer in scientific notation:
3.6x104 + 8.4x104
What is 1.2x105
3.6x104 + 8.4x104=12x104 is not in scientific notation because 12 is not less than 10
So, 12x104 = 1.2x105
Write 7,200,000,000 in scientific notation.
What is 7.2 x 109?
Arrange from least to greatest:
9.1×105, 1.2×106, 9,100,000, 8.9×105
What is 8.9×105, 9.1×105, 1.2×106, 9.1x106?
All Standard Form: 890,000, 910,000, 1,200,000, 9,100,000
All Scientific Notation:
8.9×105, 9.1×105, 1.2×106, 9.1×106
City A area = 2.5×103 km² and City B = 7.5×104 km². Which city is larger? How many times larger is it?
What is City B is 30 times larger than City A?
75/2.5=30
A library had 6.2×103 books. After a Community Book Drive, it now has 4.34×105. How many times larger is their book collection after the Book Drive?
What is 70 times larger?
434/6.2=70
Solve and show answer in scientific notation:
7.46x107 - 3.25x106
What is 7.135x107
Numbers must be adjusted so the exponents are the same before we can add OR subtract.
7.46x107 - 3.25x106 to 74.6x106 - 3.25x106 = 71.35x106 = 7.135x107 OR
7.46x107 - 0.325x107 = 7.135x107
Write 0.00053 in scientific notation.
What is 5.3 x 1/104 OR 5.3 x 10-4 ?
Arrange from least to greatest:
6.3x103, 0.0063, 630,000, 63
What is 0.0063, 63, 6.3x103, 630,000?
All Standard Form: 0.0063, 63, 6,300, 630,000
All Scientific Notation:
6.3×1/103, 6.3×101, 6.3×103, 6.3×105
Compare 8.4×104 and 2.1×103: Which number is larger and by how much?
What is 8.4×104 is 40 times larger than 2.1×103?
84/2.1=40
River C is 3.2×102 miles long. River D is 9.6×104 miles long. Which river is longer? How many times longer?
What is River D; 300 times?
960/3.2=300
Solve and show answer in scientific notation:
6.4x107 + 7.9x107
What is 1.7x107
6.4x107 + 7.9x107=14.3x107 is not in scientific notation because 14.3 is not less than 10
So, 14.3x107 = 1.43x108
Rewrite 42.7 x 106 in proper scientific notation
What is 4.27 x 107?
Arrange from least to greatest:
5.4x107, 5.04x108, 50,400,000, 540,000,000.
What is 50,400,000, 5.4x107, 5.04x108, 540,000,000?
All Standard Form: 50,400,000, 54,000,000, 504,000,000, 540,000,000.
All Scientific Notation:
5.04×107, 5.4×107, 5.04×108, 5.4×108.
Compare 7.8×108 and 2.6×106: Which number is larger and by how much?
What is 7.8×108 is 300 times larger than 2.6x106
780/2.6=300
Star A is 2.4×1012 km away. Star B is 8.0×108 km away. Which star is farther away? How many times farther?
What is Star A is 3,000 times farther than Star B?
24,000/8=3,000
Solve and show answer in scientific notation:
9.56x107 - 4.31x106
What is 9.129x107?
Numbers must be adjusted so the exponents are the same before we can add OR subtract.
Change 9.56x107 - 4.31x106 to 95.6x106 - 4.31x106 = 91.29x106 = 9.129x107 OR
Change 9.56x107 - 4.31x106 to 0.421x107 = 9.129x107