You have used place value to name the values of digits in numbers and to represent numbers in both word and grid form. Now, think back to the beginning of this lesson when you watched a video about Rita and Arjun. They wanted to buy a new game from the service offering the cheaper price. To determine which service to use, these friends can use place value to compare prices. But how?
Rita remembers comparing numbers based on their place values in her math class. She and Arjun compared the numbers 345.674 and 345.659 to determine which was greater.
Read through the information on each slide below to learn about comparing numbers as Rita and Arjun did in their math class.
Align the Numbers
Align the numbers to be compared in neat vertical columns. Notice that the decimal in each number is vertically aligned. This makes the place values of each number line up as well.
The number 345.674 stacked on top of the number 345.659. The decimals are aligned on top of each other.
Compare the Whole Number Digits
You have probably noticed that these numbers are very similar. To accurately compare them, you need to look at one digit at a time until you find where they are different. Then you will be able to determine which number has a greater or lesser value.
Look at the digits in order from left to right across the number, starting with the whole numbers.
The number 345.674 stacked on top of the number 345.659. The decimals are aligned on top of each other. The 3s have a red box around them. The 4s have a blue box around them. The 5s have a yellow box around them. The caption reads “The whole numbers (hundreds, tens, and ones) are all the same.”
Question
What do you notice about the whole number digits in each of these numbers?
They are the same.
Compare the Decimal Digits
Since the whole numbers were all the same, you can move to comparing the decimal digits.
The number 345.674 stacked on top of the number 345.659. The decimals are aligned on top of each other. The 6s have a green box around them because they are the same value.
Move on to the hundredths place.
The number 345.674 stacked on top of the number 345.659. The decimals are aligned on top of each other. The 7 in the number 345.674 and the second 5 in the number 345.659 have an orange box around them. The caption reads, “The hundredths are different. Now you can compare.
Congratulations! You have found a difference in the numbers that can be used to compare them.
The top number, 345.674, has 7 hundredths because 7 × 0.01 = 0.07.
The bottom
number, 345.659, has 5 hundredths, 5 × 0.01 = 0.05.
Question
Which number is greater, 345.674 or 345.659?
The number 345.674 is greater because 0.07 is greater than 0.05.
Show your skills!
Use what you have learned about comparing place value to answer each question below. When you think you know the answer, click each box to check your response.
Which number is greater, 1,236.705 or 1,236.507?
The number 1,236.705 is greater.
These numbers are identical until the tenths column. When comparing the digits in the tenths column, 7 tenths is greater than 5 tenths.
This means that 1,236.705
is greater than 1,236.507.
Which number is smaller, 976.054 or 976.084?
The number 976.054 is smaller.
These numbers are identical until the hundredths column. When comparing the digits in the hundredths column, 5 hundredths is less than 8 hundredths.
This means that
976.054 is smaller than 976.084.
Which number is larger, 14,609 or 14,690?
The number 14,690 is larger.
These numbers are identical until the tens place. When comparing digits in the tens column, 9 tens is larger than 0 tens. This means 14,690 is larger than 14,609.
Question
Rita and Arjun are trying to determine which online service they want to buy their new game from. One service charges $45.67, and the other charges $45.76. Which is cheaper? Explain using place value.
The service charging $45.67 is cheaper. The prices are identical until the tenths place. When comparing digits in the tenths column, 6 tenths is smaller than 7 tenths, so $45.67 is the cheaper price.
