Comparing Decimals Using Place Value Concepts

Question

Add checkmarks to complete the table.
Less than
1.61 Greater than 1.61
1 + (3 × 0.1) + (2 × 0.01)
1 + 0.7 + 0.01
1.38
All of the numbers have a 1 in the ones place.
Compare the tenths.
6 tenths is more than
3 tenths
7 tenths is more than
6 tenths
6 tenths is more than
3 tenths
• The expanded form of 1.61 is
1 + (______ × 0.1) + (1 × 0.01)
1 + 0.6 + _______

Answer 1

Let's compare the decimals and fill in the blanks.

1. Comparing the numbers:
   • The number 1.61 has 6 tenths.
   • For the number 1 + (3 × 0.1) + (2 × 0.01):
     • This simplifies to 1 + 0.3 + 0.02 = 1.32, which has 3 tenths.
     • So, 1.32 is less than 1.61.
   • For 1 + 0.7 + 0.01:
     • This simplifies to 1 + 0.7 + 0.01 = 1.71, which has 7 tenths.
     • So, 1.71 is greater than 1.61.
   • For 1.38:
     • This has 3 tenths and therefore is also less than 1.61.

Now let’s fill in the table:

• 1.32 ✅ Less than 1.61
• 1.71 ✅ Greater than 1.61
• 1.38 ✅ Less than 1.61

2. Filling in the expanded form:
   • The expanded form of 1.61 is:
     • 1 + (6 × 0.1) + (1 × 0.01)
   • So the blanks can be filled as:
     • 1 + (6 × 0.1) + (1 × 0.01)
     • 1 + 0.6 + 0.01

In summary:

• The complete sentences for the expanded form would be:
  • The expanded form of 1.61 is 1 + (6 × 0.1) + (1 × 0.01).
  • 1 + 0.6 + 0.01.