Exponents/Scientific Notation

Convert to Scientific Notation

100

0.0265

2.65*10^-2

200

392

3.92*10²

300

53,000

5.3*10⁴

400

17,000,000,000

1.7*10¹⁰

500

0.00000323

3.23*10^-6

Convert to Standard Form

100

1.92*10³

1,920

200

3.26*10⁷

32,600,000

300

4.51*10^-7

0.000000451

400

1.76*10^-3

0.00176

500

9.11*10⁵

911,000

Simplify Exponents

100

What number does x have to be?

(5⁵)^x=5⁴⁰

8

200

What number does x have to be?

5^x/5³=5⁴

7

300

Write as a single positive exponent.

(4⁶*4⁶)/4¹³

4^-1 = 1/4

400

Write as a single positive exponent.

(3⁴)⁴/3¹⁴

3²

500

Write as a single positive exponent.

(3x²)(2x⁵)(4x)

24x⁸

Multiply Scientific Notation

100

(3.5 x 10⁵)(1.2 x 10⁶)

4.2 x 10¹¹

200

(7.5 x 10⁸) (2.5 x 10⁷)

1.875 x 10¹⁶

300

(9 x 10^-5)(3 x 10⁹)

2.7 x 10⁵

400

(4.5 x 10¹¹) (2.0 x 10³)

9 x 10¹⁴

500

A giant squid weighs (5.2 x 10⁵) grams.  How many grams would a group of 5000 squids weigh?

2.6 x 10⁹

Divide Scientific Notation

100

(3.5*10⁹)/(7*10³)

5*10⁵

200

(6*10⁸)/(2*10¹⁰)

3 x 10^-2

300

(9.0  *10¹²)/(3.0 * 10⁸)

3*10⁴

400

(4.2  *10^-9)/(6.0 * 10^-3)

7 x 10^-7

500

Zubatar  has a circumference of (6.0 x 10²¹) miles and Yucay has a circumference of (1.2 x 10³²) miles.  How many times greater is Yucay’s circumference?

2.0 x 10¹⁰