5.5: Fundamentals 5 - Place value

Comparing numbers

1 Mike and Sabrina are looking at their paychecks. Mike’s take home pay is $1,578 and Sabrina’s take home pay is $1,598. Which employee had a larger take home paycheck?

To determine how large or small a number is, we need to place each digit of the number into its place value. For large numbers, digits of a number are commonly clustered by commas in groups of three, which helps to identify the place values of the digits. Each group of three numbers is called a period. The period names such as ones, thousands, millions, etc., are listed in the chart below and assist with reading and writing numbers. When reading a number, start from the left of the number, saying a period of digits one group at a time, followed by the group name.

When we compare two numbers we line up their place values.

2. Let’s explore how we can use the chart to help us determine place values.

A. To understand the value or size of the number 78429300175, first place commas to separate out the periods of the number.

B. Second, locate the digit in the hundred thousands place.

3. Write the number 3,422,710 in words. In order to do so, it is helpful to identify the periods which are separated by commas. Hint: Placing the digits in the chart may help you correctly read, and then write the number.

Whole numbers can be compared to determine which one is larger, as in problem 1. For larger numbers, to compare we need to line up the place values of each of the numbers. The number that has a digit in the left-most period is largest. If the numbers have the same number of place values, look at the first number, in the highest place value (on the left). Whichever number has the larger value in the highest place value is the largest. If that number is the same, continue looking at the next place values until you see one that is larger.

4. Compare 1,143,345 and 983,839. Explain why one whole number is larger than the other.

5. Compare 62,478 and 62,427. Explain why one whole number is larger than the other.

Comparing decimal numbers

A decimal is a number that contains a decimal point. The decimal point separates the whole number and the fractional part of the number. The whole number is to the left of the decimal point while the fractional part is to the right. The place values of decimals are related to the place values of whole numbers. The whole number part (to the left of the decimal) has the same place value as before. The place values of the digits to the right of the decimal have their own place value.

6. Looking at the place value chart from earlier, what patterns do you see in the place value names of the decimals as compared to the names of the whole numbers?

To write the name of a decimal:

Step 1: Write the whole number, as earlier in the lesson.

Step 2: Write the word “and” to represent the decimal point.

Step 3: Write the decimal portion of the number as you would if it were a whole number but end with the name of the place value of the last digit.

7. Write the numbers 12.27 and 23,754.102 out using words. Use the above chart to help you, if needed.

Numbers in our world, big and small

8. According to the US debt clock¹³, on July 27, 2018, the population of New York State was 19,742,866 people and the debt of this state was 356,265,275,579 dollars (and growing every second). Write both of these numbers out in words.

9. The largest creature to ever live on earth is the blue whale.¹⁴ A female blue whale weighs about 180,000 kilograms, which is equivalent to about 396,832.072 pounds. Write both of these numbers out in words.