Decimals and Large Numbers

Large numbers using decimals are frequently confusing to students. They tend to ignore the decimal point when they read the numbers or not know exactly what the decimal number represents. For example, the movie True Lies sold 146.3 million tickets. This is a convenient way of expressing large numbers, but it can be confusing for students. The exercises in this lesson will help students understand the large numbers. This lesson should be taught after students have learned about decimals and operations on decimals (e.g., multiplication of decimals).

Classroom Discussion and Activities

Computer Lab Activities

Classroom Discussion and Activities (Whole Group)

• Remind the students that decimals work just like fractions but they look different. In each case, they express part of a whole number. They are a relation between numbers. For example, if 4 girls in the class are wearing t-shirts and there are 10 girls in the class, then 4/10ths or .4 of the girls have t-shirts on. Use Part A of largwkst.doc to complete the exercise in converting numbers from fractions to decimals. Have the students use calculators to do the conversions.

• Focus on 1/10th as .1 for Part B of the lesson using the largwkst.doc worksheet (Multiplying by Decimals). Have students use their calculators to calculate the decimal numbers. Demonstrate on the board how 1/10th of 344 is the same as 344/10 or 344 x .1. Have students practice reading the numbers and telling what the decimal part is about. In the case of 344 x .1, we have .4 or less than 1. Use examples to make the numbers meaningful (e.g., 1/10th of 344 tickets)

• The key point to stress is that the numbers to the right of the decimal are only a part of one. Think of using a pie chart or decimal square to reinforce this

• As a final exercise, use Part B to practice rounding numbers to the 10ths place.

Computer Lab Activities

• Use Part A of the file largno.xls to get students to take the number 1,000,000 and multiply it by different decimal numbers. Create the formula for multiplying the two numbers in the first row and then COPY DOWN.

• Talk about the pattern in the numbers (from .1 to .9) and discuss how each number is a part of 1,000,000 (e.g., 1,000,000 x .7 is 700,000 or 7 tenths of 1,000,000). Have the students replace 1,000,000 with 1,000 and tell what part of 700,000 it represents.

• Part B is the key exercise. This will help students to talk about large decimal numbers. Discuss the fact that large numbers are written in decimal format because they are easier to read without those zeros. They take up less space on the paper, and are easier to understand. 34,500,000 becomes 34.5 million. To convert from decimal format back to whole number format we need to multiply both the whole number and the decimal by the unit.

• Part B presents data on movie sales and visits to national parks. Have the students break the numbers into whole numbers and decimals. They will multiple the whole numbers by 1,000,000 and the decimal numbers by 1,000,000. Discuss the results before they add them back together again. This is good practice in identifying what the decimal numbers mean.

• As a last step, take one of the numbers from the movies or national park visits. Write it in a column with its whole number on each side and then graph the three numbers. This is another way of showing how the decimal number is between the whole numbers.

For example, the numbers for the Great Smokey Mountains would be: