Powers of 10 and Scientific Notation

Prior Learning Powers of 10 &

Scientific Notation

Multiple Choice

23.1 x 10

• 0.231
• 2.31
• 231
• 2,310

Multiple Choice

17.8 ÷ 10

• 0.178

• 0.0178

• 178

• 1.78

Multiple Choice

45.89 x 100

• 45.890

• 4,589

• 0.4589

• 458.9

Multiple Choice

Which of the following expressions is equivalent to 86,000

• 86 x 10³
• 8.6 x 10²
• 860 x 10
• 8,600 x 10²

Multiple Choice

6 × 10 ²

• 60
• 600
• 6000
• 0.006

Multiple Choice

18 x 100

• 1,800
• 180
• 18,000
• 180,000

Multiple Choice

42 x 10²

• 42,000
• 420
• 420,000
• 4,200

Multiple Choice

Ms. Waites wrote the following values for powers of 10.
10² = 100
10³ = 1,000
10⁴ = 10,000
10⁵ = 100,000
Based on the pattern, which is equivalent to 100,000,000?

• 10²
• 10⁶
• 10⁷
• 10⁸

Multiple Choice

10⁰

• 0
• 1
• 10
• 100

Multiple Choice

10³

• 10
• 100
• 1000
• 30

Types of Notation

What is the same and what is different?

Scientific Notation to Decimal Notation

What is the same?

What is different?

Scientific Notation and E-Notation

looks different

means the same

Multiple Choice

Convert to standard notation:
2.4 x 10^-3 

• 2400
• 0.24
• 0.024
• 0.0024

Multiple Choice

Convert to standard notation:
3.05 x 10⁵ 

• 305,000
• 305
• 3,050,000
• 30,500

Multiple Choice

UNDERSTANDING
If the exponent is a negative number...

• you will get a large number
• you will get a small number

Multiple Choice

The rule of scientific notation is to write all exponents with a base of ____.

• 50
• 5
• 100
• 10

Multiple Choice

ANY number raised to a power of 0 will be....

• 10
• itself
• 1
• 0

Multiple Choice

UNDERSTANDING
If the exponent is a positive number...

• you will get a large number
• you will get a smaller number

Multiple Choice

Scientific Notation is made up of two number parts. The second part is a power of base 10.

• True
• False

Multiple Choice

When writing a number in scientific notation, the first number must be greater than 1, but less than 10.

• False
• True

Multiple Choice

What is scientific notation?

• A long way to write really short  numbers
• A short way to write really long numbers
• I don't know...
• None of the above

Quick Check In

After the number is in Scientific Notation, just check that:

The "digits" part is between 1 and 10 (it can be 1, but never 10)

The "power" part shows exactly how many places to move the decimal point

Multiple Choice

The closest galaxy to our own is over 2,500,000 light years away.  Write this number is scientific notation.

• 2.5 x 10⁷
• .25 x 10⁷
• 25 x 10⁵
• 2.5 x 10⁶

Multiple Choice

Light travels at a rate of 186,000 miles per second.  Write this number in scientific notation.

• 1.86 x 10⁵
• 1.86 x 10⁴
• 18.6 x 10⁴
• 186 x 10³

Multiple Choice

Which of the following is correct scientific notation?

• 20.35 x 10⁴
• .2035 x 10⁴
• 2035 ⁴
• 2.035 x10⁴

Multiple Choice

UNDERSTANDING
If the exponent is a positive number...

• you will get a large number
• you will get a smaller number

Multiple Choice

Express the following in scientific notation:
.000457

• 457 x 10⁶
• 457 x 10^-6
• 4.57 x10⁴
• 4.57 x 10^-4

Multiple Choice

How do you write
1001
in scientific notation?

• 1.0001 x 10⁴
• 1.01 x 10⁵
• 1.001 x 10³
• 10.1 x 10³

Multiple Choice

How would you write 564,000,000 in scientific notation?

• 5.64 x 10^-7
• 5.64 x 10⁶
• 5.64 x 10⁸
• 56.4 x 10⁷

Multiple Choice

7.82 x 10^-6 is an example of scientific notation. The exponent of -6 tells you your number will be very ________.

• Large
• Small
• Basic

Multiple Choice

Write 6,700 in scientific notation.

• 6.7 x 10³
• 6.7 x10^-3
• 67 x 10²
• 67 x 10^-2

Multiple Choice

Convert this number into scientific notation: 950,000

• 9.5 x 10⁵

• 9.5 x 10^-9

• 9.5 x 10²

• None of the above

Fill in the Blank

Convert this number to standard notation: 1.4 x 10^-2

Multiple Choice

Convert this number into scientific notation: 0.068

• 6.9 x 10⁶

• 6.8 x 10^-9

• 6.8 x 10^-2

• None of the above

Watch

Multiply in scientific notation

Watch

Dividing in scientific notation

Multiple Choice

(9.6×10^-8)÷(2×10^-15)

• -4.8×10⁷
• 4.8×10⁷
• 4.8×10^-7
• -4.8×10^-7

Multiple Choice

Divide:
(6.9 x 10⁷) / (2.3 x 10^-3)

• 3 x 10¹⁰
• 3 x 10⁴
• 3 x 10^-4
• 3 x 10^-11

Multiple Choice

What do you do to your exponents when you are multiplying in scientific notation?

• Subtract

• Multiply

• Divide

• Add

Multiple Choice

What do you do to your exponents when you are dividing in scientific notation?

• Subtract

• Divide

• Multiply

• Add

Multiple Choice

Multiply:
(9.4 x 10⁶)(3.2 x 10⁵)

• 30.08 x 10¹¹
• 3.8 x 10¹
• 3.008 x 10¹²
• 2.9375 x 10¹

Multiple Choice

What is the simplified version of

• 3.9 x 10⁶
• 4 x 10²⁰
• 4 x 10⁶
• 3.9 x 10²⁰

For more details

• https://youtu.be/67Lu2LJ5f2I

• https://youtu.be/vKleHlbcMSE

• https://youtu.be/AlHaA3ubIII

• and an online calculator

• https://www.calculatorsoup.com/calculators/math/scientific-notation-converter.php