Math / Numbers & Operations

QuestionPut these numbers in order from greatest to least. $19 \frac{30}{40}$ 19 0.16 $-0.65$ 19.24 Submit

Studdy Solution

STEP 1

What is this asking? We need to arrange a mix of whole numbers, decimals, and fractions from biggest to smallest. Watch out! Don't be tricked by how the numbers first appear – fractions and decimals can be bigger or smaller than whole numbers!
Also, keep an eye on those negative signs!

STEP 2

1. Convert to Decimals
2. Order Decimals
3. Final Ordering

STEP 3

Alright, let's wrangle these numbers into a form we can easily compare!
Decimals are the easiest to compare, so let's convert everything to decimals.
We've got $19 \frac{30}{40}$ , $19$ , $0.16$ , $-0.65$ , and $19.24$ .

STEP 4

First up, $19 \frac{30}{40}$ .
We can simplify the fraction $\frac{30}{40}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $10$ .
This gives us $\frac{30 \div 10}{40 \div 10} = \frac{3}{4}$ .
So, we have $19 \frac{3}{4}$ .

STEP 5

To convert $\frac{3}{4}$ to a decimal, we divide the numerator ( $3$ ) by the denominator ( $4$ ).
This gives us $3 \div 4 = 0.75$ .
So, $19 \frac{3}{4}$ becomes $19 + 0.75 = 19.75$ .
Awesome!

STEP 6

Next, we have $19$ .
This one's already a whole number, so to make it a decimal, we can just add $.00$ to the end, giving us $19.00$ .
Easy peasy!

STEP 7

$0.16$ and $-0.65$ are already decimals, so we can leave them as they are.
Finally, we have $19.24$ , which is also already a decimal.
Great! Now we have $19.75$ , $19.00$ , $0.16$ , $-0.65$ , and $19.24$ .

STEP 8

Now that all our numbers are decimals, let's line them up and see who's the biggest!
Remember, negative numbers are smaller than positive numbers, so $-0.65$ is definitely the smallest.

STEP 9

Among the positive numbers, $0.16$ is the smallest, followed by $19.00$ , then $19.24$ , and finally, $19.75$ is the largest.

STEP 10

Putting it all together from greatest to least, we have $19.75$ , $19.24$ , $19.00$ , $0.16$ , and $-0.65$ .

STEP 11

Let's convert back to the original forms of the numbers: $19 \frac{30}{40}$ , $19.24$ , $19$ , $0.16$ , and $-0.65$ .
And there we have it!

STEP 12

From greatest to least: $19 \frac{30}{40}$ , $19.24$ , $19$ , $0.16$ , $-0.65$ .

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