RWM101 Study Guide

Unit 5: Decimals

5a. Recognize the place value of decimals

  • What are the place values for decimals?

With whole numbers, we know that the location of a digit determines its value. The number 231 is really 200 + 30 + 1, because the 2 is in the hundreds place, the 3 is in the tens place, and the 1 is in the ones place.

Decimals also have place values. The first position to the right of the decimal is the tenths place, then moving to the right, you have the hundredths place, the thousandths place, the ten-thousandths place, etc. For example, the decimal .247 is 2 tenths, 4 hundredths, and 7 thousandths.

To review, see Introduction to Decimals.

5b. Apply rounding and estimation concepts with decimals

  • How do you round decimals?

When rounding decimals, there are two simple steps. First, determine the position that you want to round to and look at the digit to the right of that position. If it is a 5 or more, you round the number up, and if it is a 4 or less, you round the number down. For example, consider the number 23.4156. Let's round the number to the hundredths place. There is a 1 in the hundredths place, so we look at the digit to the right of the 1, which is a 5. Since it is 5, we round the 1 up to a 2. Therefore, the correctly rounded answer is 23.42. If, instead, the number was 23.4136, it would round down to 23.41, since the next digit is 3.

To review, see Rounding Decimals.

5c. Convert between fractions and decimals

  • How do you convert a decimal to a fraction?
  • How do you convert a fraction to a decimal?

When converting a fraction to a decimal, simply remember that a fraction is just a division problem. Divide the fraction and you will find the decimal value. For example, if you are trying to convert ¾ to a decimal, divide 3 by 4, and you will find the decimal value is .75.

When converting a decimal to a fraction, you can use your knowledge of place value to quickly convert any decimal to a fraction. For example, the decimal .23 goes to the hundredths place, making it 23 hundredths. So the decimal equivalent is 23/100. After converting to a fraction, you may need to simplify the fraction to write it in lowest terms.

To review, see Introduction to Decimals.

5d. Perform operations with decimals

  • How do you add decimals?
  • How do you subtract decimals?
  • How do you multiply decimals?
  • How do you divide decimals?

When adding or subtracting decimals, you must make sure to line up the decimal points when setting up the problem. Then you can add or subtract as you would with any other numbers. The decimal will follow in the same place in the solution.

For example:

 \begin{array}{c} 23.16 \\ +3.72 \\ \hline 26.88 \end{array}

When multiplying decimals, simply multiply the two numbers while ignoring the decimals. Once you're done, count the number of digits to the right of the decimals combined between the two numbers. Once you have multiplied, place the decimal with the same number of digits to the right as you counted. For example, when multiplying 2.4 × 3.71, simply multiply 24 × 371, then place the decimal with 3 digits to the right, since there are 3 total digits to the right of the decimal in the original problem. Therefore the answer is 8.904.

When dividing by a decimal, you want to convert the problem to one without any decimals. So when dividing 34.23 ÷ .25, you can change the problem by moving the decimal on both numbers by the same number of spaces. The goal is to make the divisor, the number you are dividing by, into a whole number. So in this case, since the divisor is .25, we want to move both the decimal 2 places to the right. This transforms our problem into 3423 ÷ 25, and therefore the answer is 136.92.

To review, see:

5e. Solve real-world and mathematical problems with decimals

  • How do you solve real-world problems with decimals?

When solving a word problem involving decimals, it is important to first understand the problem and then transform the problem correctly into an equation that you can solve. Once you have transformed the problem into an equation, you can solve it just as you would solve any other equation involving fractions.

For example, Josh has $3.45 and wants to buy some french fries for $1.09 including tax. How much will he have left over?

First, we must set up the subtraction problem, 3.45 - 1.09. Then we solve it like any subtraction problem with decimals, and the answer is $2.36.

To review, see Applications with Decimals.

Unit 5 Vocabulary

This vocabulary list includes terms listed above that students need to know to successfully complete the final exam for the course.

  • divisor 
  • place values
  • rounding