Study Sheets - Decimals

SECTION 3.4 – COMPARING AND CONVERTING DECIMALS AND
FRACTIONS.

Quick facts:

As implied in the previous sections, every fraction can be rewritten as a decimal. To do
this, just simply divide the numerator of the fraction by the denominator.

Ex. , because

And opposite, a decimal can be written as a fraction. To do this, the decimal part of the
decimal will be put in the numerator of the fraction, and the denominator will be derived
from the place value of the last digit of the number being converted.
Ex. , because the last digit (4) was on the hundredth place. This fraction can be
further simplified. Always try to find the fraction in the simplest form.

Note: If converting a decimal that contains a whole part, this whole part would become a
whole part of a mixed number.

Remember to follow the rules of conversion even for problems like:

To compare a decimal and a fraction, convert the fraction into a decimal and than
compare.

Ex. Place a symbol <, > or = between 0.165 and 1/6

Answer: Because 1/6 is equal to approximately 0.166, which is greater than 0.165, we can
say:

Test yourself:

Convert to a decimal:

,round to the nearest hundredth = 3.67 , round to the nearest thousandth

Convert to a fraction:

Place a correct symbol between the numbers:

Challenge Yourself:
It might be useful for the future for you to know the basic conversions between fractions
and decimals, as they are widely used in real life. Think of change, for example a quarter
(which is $ 1/4), can be also written as $0.25.

Getting accustomed with the conversion table (that you can find in Appendix of this
chapter) simplifies the process of converting fractions to decimals by eliminating of the
repetitive dividing.

Assignment:
Textbook Chapter 3.6 (p.162): Exercises 1 – 69 every fourth problem