Question

Rewrite in descending order.
1) $6.4,6.46,0.646,4.66$
2) $9.21,19.2,2.91,1.29$
3) $8.62,86.2,0.82,862.0$

Answer 1

Hint: To write in descending order means writing from largest to the smallest. The largest and smallest numbers can be found by comparing the whole part, the tenth part, the hundredth part, and so on. In each part, we have to check which is the greatest and if this is the same proceed to the next part.

Complete step by step answer:
Here we are given three sets of decimals. We are asked to write in descending order. This means we have to rearrange the numbers in such a way that the first one is the largest among them and the second one is the second-largest and so on. Thus we get the smallest number at the end.
For finding the largest and smallest, we must have some ideas about decimals.
A number has two parts. We can call them the whole part and the decimal part.
For integers like $1,2,3...$, the decimal part is absent. So we call these numbers as whole numbers.
The decimal part is that one which appears after the decimal point.
A number is greater than another if the whole part of the former is greater than that of the latter, no matter what the decimal part is. If the whole part of the two numbers is the same, we can compare it for the decimal part.
The first digit on the decimal part is called the tenth part, the second digit the hundredth part, and so on.
We can consider one by one.

1) $6.4,6.46,0.646,4.66$
Here the first two numbers have the whole part $6$ and the next two numbers have the whole part $0,4$.
So we can say directly that the first two numbers are greater than rest two and further $4.66 > 0.646$.
Now consider $6.4$ and $6.46$. Here the whole part as well as the tenth part is the same.
If we represent as fractions we get, $6.4 = 6 + \dfrac{4}{{10}}$ and $6.46 = 6 + \dfrac{4}{{10}} + \dfrac{6}{{100}}$.
This gives $6.46 > 6.4$

$\therefore$ The required answer: $6.46 > 6.4 > 4.66 > 0.646$

2) $9.21,19.2,2.91,1.29$
Here using the same way we get,
$9.21 = 9 + \dfrac{2}{{10}} + \dfrac{1}{{100}}$
$19.2 = 19 + \dfrac{2}{{10}}$
$2.91 = 2 + \dfrac{9}{{10}} + \dfrac{1}{{100}}$
$1.29 = 1 + \dfrac{2}{{10}} + \dfrac{9}{{100}}$

$\therefore$ The required answer: $19.2 > 9.21 > 2.91 > 1.29$

3) $8.62,86.2,0.82,862.0$
Here,
$8.62 = 8 + \dfrac{6}{{10}} + \dfrac{2}{{100}}$
$86.2 = 86 + \dfrac{2}{{10}}$
$0.82 = 0 + \dfrac{8}{{10}} + \dfrac{2}{{100}}$
$862.0 = 862 + \dfrac{0}{{10}} = 862$
Comparing we have $862 > 86.2 > 8.62 > 0.82$

$\therefore$ The required answer: $862 > 86.2 > 8.62 > 0.82$

Note:
The reverse order of descending is called ascending, which is from smallest to largest. Also, the trailing zeros if any at the end of the decimal doesn’t increase or decrease the decimal value. But zeros which appear immediately after the decimal point and precede a non-zero number decrease the number value.