Algebra Know-It-ALL

162 Review Questions and Answers

Answer 7-7

A calculator can be used for this purpose, but it must be able to display a lot of digits! Other-

wise, old-fashioned long division is the best way to find these:

1/2 = 0.5

1/3 = 0.333333333333 ...

1/4 = 0.25

1/5 = 0.2

1/6 = 0.166666666666 ...

1/7 = 0.142857142857 ...

1/8 = 0.125

1/9 = 0.111111111111 ...

1/10 = 0.1

Question 7-8

How can we write the endless repeating decimal 0.458745874587... as a fraction?

Answer 7-8

First, we must identify the sequence of digits that repeats. Here, it’s 4, 5, 8, and 7. There are

four digits in the sequence, so we create a fraction with a denominator having four digits, all 9s.

Then we make the repeating sequence into a four-digit numeral and use it as the numerator

of the fraction. That gives us

0.458745874587...= 4,587/9,999

Question 7-9

How can we make a decimal expression an order of magnitude larger or smaller?

Answer 7-9

To make it an order of magnitude larger, move the decimal point to the right by one place. To

make it an order of magnitude smaller, move the decimal point to the left by one place. Here’s

an example. Start with

35,468.0337

To make this number an order of magnitude (or factor of 10) larger, we must multiply by 10.

That’s done by moving the decimal point to the right by one place and then repositioning the

comma, getting

354,680.337