57
Comparing decimal fractions
Textbook: Part 2, lesson 57, pp. 80–83
GoalCompare decimals; equal decimals; show decimals on the number ray.
New words
equal decimals · teng o‘nli kasrlarplace · xonanumber ray · sonlar nuricomparison · taqqoslash
Explanation
If we write zeros to the right of a decimal or remove zeros from its right end, the number does not change: 0.8 = 0.80 = 0.800. To compare two decimals, first make the number of digits after the point equal by adding zeros, then drop the points and compare the resulting natural numbers. Another way: compare the whole parts first; if they are equal, compare tenths, then hundredths and so on from left to right. On the number ray the larger decimal lies to the right and the smaller to the left, while equal decimals are shown by one point.
Worked examples
4.7 and 4.65: 4.70 and 4.65 → 470 > 465, so 4.7 > 4.65. The equal whole parts and tenths 7 > 6 show the same.
The points 0.3, 0.45 and 0.5 lie on the number ray from left to right in this order, because 0.30 < 0.45 < 0.50.
Class activity
“Marking points”: draw a number ray in your notebook with a 10-square unit segment, mark 0.2, 0.7, 1.3 and 1.9 and read them in increasing order.
Practice
1
Compare: 6.09 and 6.1.
6.09 < 6.1
2
Which is larger: 0.45 or 0.405?
0.45
3
Write 12.30 without the final zero.
12.3
4
Why is 0.7 = 0.70?
Seven tenths equal seventy hundredths, because 7/10 = 70/100.