Decimal positions: place value, comparison and distance
Before you start: Read whole numbers and locate them on a number line.
What changes to the right of the decimal point?
Each step to the right divides a place's value by 10. In 3.47, the 3 means three whole units, the 4 means four tenths and the 7 means seven hundredths. Thus 3.47 = 3 + 4/10 + 7/100. The digits describe quantities, not just a string of symbols.
Locate a decimal by zooming in
To find 2.36, first locate the interval from 2 to 3. Split it into ten equal parts and find 2.3. Then split the interval from 2.3 to 2.4 into ten equal parts. Move six of those hundredth-steps from 2.3 to reach 2.36. This explains why a finer scale is needed for hundredths.
Compare aligned place values
Compare 0.7 and 0.65 by writing 0.7 as 0.70. Both are now in hundredths: 70 hundredths is more than 65 hundredths, so 0.7 > 0.65. A longer decimal is not automatically larger. Adding a trailing zero preserves value because 7/10 = 70/100.
Find a gap and distinguish it from a position
If your current position is 2.36 and the target is 2.50, subtract aligned places: 2.50 − 2.36 = 0.14. That is 14 hundredth-steps or one tenth plus four hundredths. Check by adding: 2.36 + 0.14 = 2.50. The target position is 2.50; the required change is 0.14.
For negative positions, moving right still increases the value: −0.2 is greater than −0.5 because it is closer to zero on the right. A larger absolute distance from zero does not always mean a greater number.
Try it yourself
Which is greater, 4.08 or 4.8? How far is 4.08 from a target at 4.50?
Show answer and explanation
4.8 = 4.80, so 4.8 is greater. The gap is 4.50 − 4.08 = 0.42. Check: 4.08 + 0.42 = 4.50.
Use the activity to check your understanding
Use coarse movements to approach a target and fine movements to finish. Describe each movement in tenths or hundredths.