Decimal Numbers

Decimal numbers extend the place-holder idea that we use with regular numbers. For example, in 472 we
have 4 hundreds, 7 tens, and 2 ones, or

(1) 472 = 4 · 100 + 7 · 10 + 2 · 1

In a decimal number like 43.58, we have 4 tens, 3 ones, 5 tenths, and 8 hundredths, or
(2)

The dot, the decimal point, just tells us where the ones and tenths are. We won’t be doing any by-hand
additions , but if you do, you need to line up the decimal point so that the tenths get added to tenths,
hundredths to hundredths, etc.

One big advantage is that all decimal numbers can be treated the same. Unlike with fractions , like 1/3 and 1/5 ,
where we have to find a common denominator to add them. Partly because of this, calculators like decimal
numbers, and that’s a big advantage too.

Converting to fractions

Converting to fractions
Since a decimal number is the sum of whole numbers and fractions, it’s pretty easy to write a decimal number
in its fraction form . For example, the 43.58 is

(3)

The smallest fraction, the hundredths in this case, will work as a common denominator . We can write this
as
(4)

More concisely, multiplying by 100 (which has two zeros) moves two decimal places past the decimal point.
So for 37.9076, we would do

(5)

Converting from fractions to decimals

With a calculator , converting to decimals is easy. We just compute the division that the fraction represents.
For example, to find that
(6)

you just do 7 ÷ 8 on your calculator .

The big problem with decimal numbers is that we regularly run into decimal numbers with infinitely many
non- zero digits . For example, if we do 5 ÷ 7, we get

(7)

We can’t even write down all the digits. In cases like this , we generally do something called rounding. I will
usually ask you to round your answer to a certain number of decimal places. For example, if I say round to
four decimal places, then you will write a number with four digits to the right of the decimal point. In this
case, we would get
(8)

Note that the next digit after the 2 was an 8, so we rounded up to a 3. Remember that if the next digit is a
5 or more, then we round up. The funny “≈ ” means approximately equal to. We won’t worry to much about
using the approximately- equal sign , but always remember that when you round, you’re a little off from the
actual number.

Here are a few examples where we convert to decimals and round to four decimal places.

In these, we’ll round to two decimal places.

1. Convert 12.099 to a fraction.
2. Convert 102.5 to a fraction.
3. Convert 722.344 to a fraction.
4. Convert 15.14 to a fraction.
5. Convert 92.7 to a fraction.
6.Convertto a decimal number, and round to four decimal places (if you have to).
7. Convert5/12to a decimal number, and round to four decimal places.
8. Convert9/14 to a decimal number, and round to four decimal places.
9. Convert12/5 to a decimal number, and round to two decimal places (if you have to).
10. Convert3/8 to a decimal number, and round to two decimal places. although we
would probably just leave this at 0.375, since this is exact and short.

1. Homework 05

When converting decimals to fractions, use the smallest power of ten that is necessary. That’s the only
answer I’ll have in Blackboard. When rounding, be sure to round correctly. For example, if the next digit is
a 5 or greater, you should round up.

1. Convert 15.99 to a fraction.

2. Convert 1022.53 to a fraction.

3. Convert 2.3 to a fraction.

4. Convert 11.1111 to a fraction.

5. Convert 0.01 to a fraction.

6. Convert 0.0011 to a fraction.
7. Convert to a decimal number, and round to four decimal places (if you have to).
8. Convert to a decimal number, and round to four decimal places.
9. Convert to a decimal number, and round to six decimal places.
10. Convert to a decimal number, and round to four decimal places.
11. Convert to a decimal number, and round to two decimal places.
12. Convert to a decimal number, and round to two decimal places.

13. Convert 3.2 to a fraction.
14. Convert to a decimal number, and round to four decimal places.

15. Convert 17.3344 to a fraction.

16. Convert 12.70035 to a fraction.
17. Convertto a decimal number, and round to four decimal places.
18. Convertto a decimal number, and round to four decimal places (if you need to).
19. Convert to a decimal number, and round to four decimal places.

20. Convert 1534.2233 to a fraction.