Numbers worth knowing by heart · Study guide · Sol Rising

Numbers worth knowing by heart

Recognizing these on sight turns a lot of questions into one step.

Squares

1^{2} = 1

2^{2} = 4

3^{2} = 9

4^{2} = 16

5^{2} = 25

6^{2} = 36

7^{2} = 49

8^{2} = 64

9^{2} = 81

10^{2} = 100

11^{2} = 121

12^{2} = 144

13^{2} = 169

14^{2} = 196

15^{2} = 225

16^{2} = 256

17^{2} = 289

18^{2} = 324

19^{2} = 361

20^{2} = 400

21^{2} = 441

22^{2} = 484

23^{2} = 529

24^{2} = 576

25^{2} = 625

Cubes

1^{3} = 1

2^{3} = 8

3^{3} = 27

4^{3} = 64

5^{3} = 125

6^{3} = 216

7^{3} = 343

8^{3} = 512

9^{3} = 729

10^{3} = 1,000

Powers of 2

2^{0} = 1

2^{1} = 2

2^{2} = 4

2^{3} = 8

2^{4} = 16

2^{5} = 32

2^{6} = 64

2^{7} = 128

2^{8} = 256

2^{9} = 512

2^{10} = 1,024

2^{11} = 2,048

2^{12} = 4,096

Primes below 100

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

There are 25 of them. 1 is not prime, and 2 is the only even prime.

Fractions, decimals, and percents

Fraction	Decimal	Percent
$\frac{1}{2}$	0.5	50%
$\frac{1}{3}$	0.3	$33 \frac{1}{3}$ %
$\frac{2}{3}$	0.6	$66 \frac{2}{3}$ %
$\frac{1}{4}$	0.25	25%
$\frac{3}{4}$	0.75	75%
$\frac{1}{5}$	0.2	20%
$\frac{2}{5}$	0.4	40%
$\frac{3}{5}$	0.6	60%
$\frac{4}{5}$	0.8	80%
$\frac{1}{6}$	0.16	$16 \frac{2}{3}$ %
$\frac{5}{6}$	0.83	$83 \frac{1}{3}$ %
$\frac{1}{8}$	0.125	$12 \frac{1}{2}$ %
$\frac{3}{8}$	0.375	$37 \frac{1}{2}$ %
$\frac{5}{8}$	0.625	$62 \frac{1}{2}$ %
$\frac{7}{8}$	0.875	$87 \frac{1}{2}$ %
$\frac{1}{9}$	0.1	$11 \frac{1}{9}$ %
$\frac{1}{10}$	0.1	10%
$\frac{1}{12}$	0.083	$8 \frac{1}{3}$ %

A bar means the digits under it repeat forever. Eighths go up by 0.125 each: 1/8 = 0.125, 2/8 = 0.25, 3/8 = 0.375, and so on.

AFOQT questions on this: Perfect squares · Square roots · Decimals to fractions · Ordering fractions

Drill it

Quick questions on just this skill, to build speed before the practice tests. Type the answers; a clock keeps your time.

Squares 1² to 25². $11^{2}$ = ?
Square roots Of the perfect squares to 625. $\sqrt{121}$ = ?
Cubes and powers of 2 Up to 10³ and 2¹². $2^{3}$ = ?
Fractions and decimals 3/8 is 0.375, and back. Write $0.375$ as a fraction.
Fractions as percents 1/8 is 12.5%; 1/3 is 33 1/3%. $\frac{1}{6}$ as a percent

Questions 1 to 50 Check answers as I type Leave the answers off the PDF