Ch 1 Digits and Decimals

Question 1

How many digits are there in the number system?

Answer 1

10 digits- 0,1,2,3,4,5,6,7,8,9

Question 2

List the place values?

Answer 2

1 million, 100 thousand, 10 thousand, 1 thousand, hundreds, tens, units/ones . tenth, hundredth, thousandth

Question 3

Using the power of 10, list the place values?

Answer 3

thousand, hundred, ten, one, tenth, hundredth, thousandths 1000 100 10 1 .1 .01 .001

10³ 10² 10¹ 10⁰ 10^-1 10^-2 10^-3

Question 4

What are the rules for multiplying a # by a positive power of 10?

Answer 4

Move the decimal to the right the specified # of places b/c this makes the positive number larger.

Ex- 3.9742*10³ = 3,974.2 (move the decimal to the right 3 places)

Ex- 89.507*10 = 895.07 (move the decimal to the right 1 place)

Question 5

What are the rules for dividing a # by a positive power of 10?

Answer 5

Move the decimal to the left the specified # of places b/c this makes the positive number smaller.

Ex- 4,169.2/10² = 41.692 (move the decimal to the left 2 places)

Ex- 89.507/10 =8.9507 (move the decimal to the left 1 place)

Question 6

Solve the following by shifting decimal using power of 10?

Answer 6

Ex - 2.57*10⁶ = 2,570,000 ( add 4 zeroes at the end)

Ex - 14.29/10⁵ = . 0001429 (add 3 zeroes at the beg)

Question 7

Solve the following using negative powers of 10?

Answer 7

6,782.01*10^-3 = 6.78201 ( Multiplication switches to division and for division, we have to move decimal to the left)

Ex- 53.0447/10^-2 = 5,304.47 ( division switches to multiplication and for multiplication, we have to move decimal to the right)

Question 8

What is .0003*40,000?

Answer 8

Shortcut - Multiplyingvery large number and a very small number; move the decimals in theopposite direction the same number of places.

Division - move the decimal in the same direction.

.0003 - move the decimal 4 places to the right = 3

40,000 - move the decimal 4 places to the left = 4

3* 4 = 12

Question 9

What is .0045/.09?

Answer 9

Shortcut - division problems that involve decimals, shift the decimal point in the same direction in both divisor and the dividend.

Multiplication - move the decimal in the opposite direction.

.0045/.09 = 45/900 - (move the decimal 4 spaces to the right to make both the num and den whole #’s)

45/900 = .05

Question 10

What is (.5)⁴?

Answer 10

.5 = 5*10^-1

rewrite the decimal as power of 10

(5*10^-1)⁴ = 5⁴ * 10^-4 ( apply the exponent to each part)

5⁴= 25²= 625 (compute the first part and combine)

625 * 10^-4= .0625

Question 11

What is 3√.000027

Answer 11

.000027 = 27*10^-6 (.000027)^1/3 = (27*10^-6)^1/3 (write the root as of fractional exponent as power of 10)

(27) ^1/3 * (10^-6)^1/3 = (27)^1/3 * 10^-2 (Apply the exponent to each part)
(27) ^1/3= 3 (since 3³=27)

Compute the first part and combine 3*10^-2=.03

Question 12

Solve the following using shortcut?

Answer 12

Ex (.04)³= (.04)³ (2 decimal places * 3 = 6 places)

= .000064 (6 places)

Ex 3√.000000008 = .002 ( 3 decimal places)

= 3√.000000008 is 9 decimal places ( 9 decimal places/3 = 3 decimal places)