Decimals

Decimals are used to denote non-integer, ‘partial’ quantities. Decimals are directly related to fractions and percentages as shown below.

When working with decimals using a calculator, you can enter and treat them just like integers; the same rules of addition, subtraction, multiplication, and division all apply. Since calculators are permitted on the COMPASS Test, it is not necessary for you to practice multiplying and dividing decimal numbers by hand.

To convert a fraction into a decimal using your calculator just preform the division implied by the fraction. For example:

One time-saving trick to know about decimals involves multiplying or dividing by powers of ten. If you multiply any number by 10, just move the decimal place once to the right. Examples:

If you divide by 10, move the decimal place once to the left:

If you multiply by 100, you are multiplying by 10 twice since 10\cdot10=100, so you move the decimal place two spots to the right:

This rule applies when multiplying and dividing by any powers of ten (10,100,1000, 10000,…).

Because of the exclusive relationship 10 has to our base 10 numbering system, the decimal places are each referred to by their relationship to the powers of ten. For the number: 31.587, 5 is in the tenths place, 8 is in the hundredths place, and 7 is in the thousandths place.

If you were asked to round 31.587 to the nearest hundredth you would round it to 31.59. You essentially chop off everything past the hundredths place, and adjust the number in the hundredths place up 1 if the number in the thousandths place is greater than or equal to 5. Use a calculator as needed. Round to the nearest hundredth.

Practice questions

Convert the following fractions to decimal numbers

1. \( \frac{5}{7} \)
2. \( \frac{7}{5} \)
3. \( 3 \frac{3}{5} \)
4. \( \frac{13}{4} \)

Solve

5. \( 12.41\cdot3.5 \)
6. \( 211.7/19.4 \)
7. Paul has \( 12.75 \) cups of rice. His wife Susan brings home \( 2\frac{3}{4} \) cups from the store. They then eat \( 5.8 \) cups of rice during the week. How much rice do they have left?
8. Mick buys \( 4 \) movie tickets for \( $7.25 \) each. He then buys \( 2 \) sodas for \( $3.50 \) each, \( 1 \) popcorn for \( $2.65 \), and \( 3 \) boxes of candy for \( $1.89 \) each. How much money has Mick spent?

Solutions

1. \( \frac{5}{7}\approx 0.71 \)
2. \( \frac{7}{5}=1.4 \)
3. \( 3 \frac{3}{5}=3.6 \)
4. \( \frac{13}{4}=3.25 \)
5. \( 12.41\cdot3.5\approx 43.44 \)
6. \( 211.7/19.4\approx 10.91 \)
7. \( 12.75+2.75-5.8=9.7 \)
8. Solution: $$ \begin{align*} & 4\cdot 7.25+2\cdot 3.5+2.65+3\cdot 1.89 \\ & =29+7+2.65+5.67 \\ & =44.32 \end{align*} $$